28 + Interview Questions in ANGLES IN GENERAL AWARENESS Page 1 InterviewSolution

1.	Name the points :(i) in the interior of the angle PQR,(ii) in the exterior of the angle PQR.
Answer» (i) a, b and x (ii) d, m, n, s, and t.

1.

Name the points :(i) in the interior of the angle PQR,(ii) in the exterior of the angle PQR.

Answer»

(i) a, b and x

(ii) d, m, n, s, and t.

Discussion

2.	The measures of two supplementary angles are (3x + 15)° and (2x + 5)°. Find x.
Answer» We know that, sum of two supplementary angles = 180° ∴ (3x + 15)° + (2x + 5)° = 180° ‘ 3x + 15 + 2x + 5 = 180° ⇒ 3x + 2x + 15 + 5 = 180° ⇒ 5x°+ 20° = 180° ⇒ 5x = 180° – 20° ⇒ 5x = 160° ⇒ x = (160/5)° ⇒ x = 32°

2.

The measures of two supplementary angles are (3x + 15)° and (2x + 5)°. Find x.

Answer»

We know that, sum of two supplementary angles = 180°

∴ (3x + 15)° + (2x + 5)° = 180° ‘

3x + 15 + 2x + 5 = 180°

⇒ 3x + 2x + 15 + 5 = 180°

⇒ 5x°+ 20° = 180°

⇒ 5x = 180° – 20°

⇒ 5x = 160°

⇒ x = (160/5)°

⇒ x = 32°

Discussion

3.	In the given figure, PQR is a straight line. Find x. Then complete the following:(i) ∠AQB = ……..(ii) ∠BQP = ……..(iii) ∠AQR = …….
Answer» PQR is a straight line ∠AQP=x + 20° ∠AQB = 2x + 10° ∠BQR = x – 10° But ∠AQP + ∠AQB + ∠BQR = 180° ⇒ x + 20° + 2x + 10° + x-10°= 180° ⇒ 4x + 20°= 180° ⇒ 4x= 180°- 20°= 160° ⇒ x = (160/4)° = 40° (i) ∠AQB = 2x + 10° = 2 x 40° + 10° = 80° + 10° = 90° ∠AQP = x + 2(T = 40° + 20° = 60°) ∠BQR = x – 10° = 40° – 10° = 30° (ii) ∠BQP = ∠AQP + ∠AQB = 60° + 90° = 150° (iii) ∠AQR = ∠AQB + ∠BQR = 90° + 30° = 120°

3.

In the given figure, PQR is a straight line. Find x. Then complete the following:(i) ∠AQB = ……..(ii) ∠BQP = ……..(iii) ∠AQR = …….

Answer»

PQR is a straight line

∠AQP=x + 20°

∠AQB = 2x + 10°

∠BQR = x – 10°

But ∠AQP + ∠AQB + ∠BQR = 180°

⇒ x + 20° + 2x + 10° + x-10°= 180°

⇒ 4x + 20°= 180°

⇒ 4x= 180°- 20°= 160°

⇒ x = (160/4)° = 40°

(i) ∠AQB = 2x + 10° = 2 x 40° + 10° = 80° + 10° = 90°

∠AQP = x + 2(T = 40° + 20° = 60°)

∠BQR = x – 10° = 40° – 10° = 30°

(ii) ∠BQP = ∠AQP + ∠AQB = 60° + 90° = 150°

(iii) ∠AQR = ∠AQB + ∠BQR = 90° + 30° = 120°

Discussion

4.	In the given diagram, ABC is a straight line.(i) If x = 53°, find y.(ii) If y =1 1/2 right angles ; find x.
Answer» (i) From the figure, ∠ABD + ∠DBC = 180° (Linear pair of angles) ⇒ x + y = 180° ⇒ 53°+ y = 180° (∵ x = 53”) ⇒ y = 180° – 53° ⇒ y = 127° (ii) From figure again, x + y = 180° 1 + 3/2 x 90 = 180° ⇒ x + 1 1/2 right angles = 180° ⇒ x + 3/2 x 90 =180° ⇒ x + 135°= 180° ⇒ x = 180° – 135° ⇒ x = 45°

4.

In the given diagram, ABC is a straight line.(i) If x = 53°, find y.(ii) If y =1 1/2 right angles ; find x.

Answer»

(i) From the figure,

∠ABD + ∠DBC = 180° (Linear pair of angles)

⇒ x + y = 180°

⇒ 53°+ y = 180° (∵ x = 53”)

⇒ y = 180° – 53°

⇒ y = 127°

(ii) From figure again,

x + y = 180°

1 + 3/2 x 90 = 180°

⇒ x + 1 1/2 right angles = 180°

⇒ x + 3/2 x 90 =180°

⇒ x + 135°= 180°

⇒ x = 180° – 135°

⇒ x = 45°

Discussion

5.	Explain what do you understand by :(i) Adjacent angles ?(ii) Complementary angles ?(iii) Supplementary angles ?
Answer» (i) Adjacent Angles: Two angles are called adjacent angles if (a) they have a common vertex (b) they have one common arm and (iii) the other two arms of the angles are on the opposite sides of the common arm. (ii) Complementary Angles : Two angles whose sum is 90° are called complementary angles to each other. (iii) supplementary angles:: Two angles whose sum.is 180° are called supplementary angles to each other.

5.

Explain what do you understand by :(i) Adjacent angles ?(ii) Complementary angles ?(iii) Supplementary angles ?

Answer»

(i) Adjacent Angles: Two angles are called adjacent angles if (a) they have a common vertex (b) they have one common arm and (iii) the other two arms of the angles are on the opposite sides of the common arm.

(ii) Complementary Angles : Two angles whose sum is 90° are called complementary angles to each other.

(iii) supplementary angles:: Two angles whose sum.is 180° are called supplementary angles to each other.

Discussion

6.	Two complementary angles are in the ratio 7 : 8. Find the angles.
Answer» Let two complementary angles are 7x and 8x ∴ 7x + 8x = 90° ⇒ 15x = 90° ⇒ x = (90/15) ° ⇒ x = 6° ∴ Two complementary angles are 7x = 7 x 6° = 42° 8x = 8 x 6° = 48°

6.

Two complementary angles are in the ratio 7 : 8. Find the angles.

Answer»

Let two complementary angles are 7x and 8x

∴ 7x + 8x = 90°

⇒ 15x = 90°

⇒ x = (90/15) °

⇒ x = 6°

∴ Two complementary angles are

7x = 7 x 6° = 42°

8x = 8 x 6° = 48°

Discussion

7.	The measures of two complementary angles are (2x – 7)° and (x + 4)°. Find x.
Answer» We know that, sum of two complementary angles = 90° ∴ (2x – 7) + (x + 4) = 90° 2x - 7 + x + 4 = 90° ⇒ 2x + x – 7 + 4 = 90° ⇒ 3x – 3 = 90° ⇒ 3x = 90 + 3 ⇒ 3x = 93 ⇒ x = 93/3 x = 31

7.

The measures of two complementary angles are (2x – 7)° and (x + 4)°. Find x.

Answer»

We know that, sum of two complementary angles = 90°

∴ (2x – 7) + (x + 4) = 90°

2x - 7 + x + 4 = 90°

⇒ 2x + x – 7 + 4 = 90°

⇒ 3x – 3 = 90°

⇒ 3x = 90 + 3

⇒ 3x = 93

⇒ x = 93/3

x = 31

Discussion

8.	For an angle x°, find :(i) the complementary angle(ii) the supplementary angle(iii) the value of x° if its supplementary angle is three times its complementary angle.
Answer» For an angle x, (i) Complementary angle of x° = (90° – x) (ii) Supplementary angle of x° = (180° – x) (iii) ∵ ‘Supplementary angle = 3 (complementary anlge) 180°- x = 3 (90°-x) ⇒ 180°- x = 270°- 3x ⇒-x + 3x = 270°-180° ⇒ 2x = 90° ⇒x= (90/2)°= 45° ∴ x = 45°

8.

For an angle x°, find :(i) the complementary angle(ii) the supplementary angle(iii) the value of x° if its supplementary angle is three times its complementary angle.

Answer»

For an angle x,

(i) Complementary angle of x° = (90° – x)

(ii) Supplementary angle of x° = (180° – x)

(iii) ∵ ‘Supplementary angle = 3 (complementary anlge)

180°- x = 3 (90°-x)

⇒ 180°- x = 270°- 3x

⇒-x + 3x = 270°-180°

⇒ 2x = 90°

⇒x= (90/2)°= 45°

∴ x = 45°

Discussion

9.	In the given figure; AB, CD and EF are straight lines. Name the pair of angles forming :(i) straight line angles.(ii) vertically opposite angles.
Answer» In the given figure, AB, CD, and EF are straight lines on intersecting, angles are formed a, b, c, d, l, m, n, and p. (i) In the figure pairs of straight line angles are ∠a, ∠b; ∠b, ∠c; ∠c, ∠d; ∠d, ∠a ∠l, ∠m; ∠m, ∠n;∠n, ∠p, and ∠p, ∠l (ii) Pairs of vertical angles are ∠a, ∠c; ∠b, ∠d; ∠l, ∠n; ∠m, ∠p

9.

In the given figure; AB, CD and EF are straight lines. Name the pair of angles forming :(i) straight line angles.(ii) vertically opposite angles.

Answer»

In the given figure, AB, CD, and EF are straight lines on intersecting, angles are formed a, b, c, d, l, m, n, and p.

(i) In the figure pairs of straight line angles are ∠a, ∠b; ∠b, ∠c; ∠c, ∠d; ∠d, ∠a ∠l, ∠m; ∠m, ∠n;∠n, ∠p, and ∠p, ∠l

(ii) Pairs of vertical angles are ∠a, ∠c; ∠b, ∠d; ∠l, ∠n; ∠m, ∠p

Discussion

10.	Example for obtuse angle.(1) 90°(2) 53°(3) 178°(4) 180°
Answer» (3) 178° – Obtuse Angle

Discussion

11.	Write the complement angle of :(i) 45°(ii) x°(iii) (x – 10)°(iv) 20° + y°
Answer» (i) Complement angle of 45° = 90° – 45° = 45° (ii) Complement angle of x° = 90° – x° = (90 – x)° (iii) Complement angle of (x – 10)° = 90° (x – 10°) = 90°- x + 10° = 100°-x (iv) Complement angle of 20° + y° = 90°- (20°+ y°) = 90° – 20° -y° = 70° - y°

11.

Write the complement angle of :(i) 45°(ii) x°(iii) (x – 10)°(iv) 20° + y°

Answer»

(i) Complement angle of 45°

= 90° – 45° = 45°

(ii) Complement angle of x°

= 90° – x° = (90 – x)°

(iii) Complement angle of (x – 10)° = 90° (x – 10°)

= 90°- x + 10° = 100°-x

(iv) Complement angle of 20° + y°

= 90°- (20°+ y°)

= 90° – 20° -y° = 70° - y°

Discussion

12.	Give two examples of parallel lines you can see in your environment.
Answer» (i) Bars on the window. (ii) Horizontal lines in the notebook are the examples of parallel lines.

12.

Give two examples of parallel lines you can see in your environment.

Answer»

(i) Bars on the window.

(ii) Horizontal lines in the notebook are the examples of parallel lines.

Discussion

13.	Give two examples of perpendicular lines you can see in your environment.
Answer» (i) The angles formed by a pole and its shadow on the ground. (ii) The adjacent sides of a notebook.

13.

Give two examples of perpendicular lines you can see in your environment.

Answer»

(i) The angles formed by a pole and its shadow on the ground.

(ii) The adjacent sides of a notebook.

Discussion

14.

Match the following:Measure of theangleType of the anglei. 180°a. Zero angleii. 240°b. Straight angleiii. 360°c. Reflex angleiv. 0°d. Complete angle

Answer»

Completed table:

Measure of the angle	Type of the angle
i. 180°	b. Straight angle
ii. 240°	c. Reflex angle
iii. 360°	d. Complete angle
iv. 0°	a. Zero angle

Discussion

15.	Say, true or false of the following:i. Parallel lines do not intersect each other.ii. Pole and its shadow on the ground makes a cute angle.iii. Angle between two parallel lines is 90°.iv. Angle between two intersecting lines may or may not be 90°.
Answer» i. True ii. False iii. False iv. True

15.

Say, true or false of the following:i. Parallel lines do not intersect each other.ii. Pole and its shadow on the ground makes a cute angle.iii. Angle between two parallel lines is 90°.iv. Angle between two intersecting lines may or may not be 90°.

Answer»

i. True

ii. False

iii. False

iv. True

Discussion

16.

Complete the following table:AngleName of the angleVertex of the angleArts of the angle

Answer»

Sr. No.	i.	ii.	iii.
Name of the angle	∠PYR or ∠RYP	∠LMN or ∠NML	∠BOS or ∠SOB
Vertex of the angle	Y	M	O
Arms of the angle	YP and YR	ML and MN	OB and OS

Discussion

17.	Look at the pictures below and identify the different types of angles.
Answer» i. Complete angle ii. Reflex and Acute angle iii. Acute and Obtuse angle

17.

Look at the pictures below and identify the different types of angles.

Answer»

i. Complete angle

ii. Reflex and Acute angle

iii. Acute and Obtuse angle

Discussion

18.	Look at the figures below and write the type of each of the angles:
Answer» a. Acute angle b. Right angle c. Reflex angle d. Straight angle e. Zero angle f. Complete angle

18.

Look at the figures below and write the type of each of the angles:

Answer»

a. Acute angle

b. Right angle

c. Reflex angle

d. Straight angle

e. Zero angle

f. Complete angle

Discussion

19.	Measure the angles given below and write the measure in the given blanks. ......... ........ ......... . ...... .
Answer» (1) 40° (2) 120° (3) 90° (4) 85°

19.

Measure the angles given below and write the measure in the given blanks. ......... ........ ......... . ...... .

Answer»

(1) 40°

(2) 120°

(3) 90°

(4) 85°

Discussion

20.	For each angle given below, write the name of the vertex, the names of the arms and the name of the angle.
Answer» (i) In figure (i) O is the vertex, OA, OB is its arms and name of the angle is ∠AOB or∠BOA or simply ∠O. (ii) In figure (ii) Q is the vertex, QP and QR its arms and the name of the angle is ∠PQR or ∠RQP or simply ∠Q. (iii) In figure (iii), M is the vertex, MN and ML and its anus, and the name of the angle is ∠LMN or ∠NML or simply ∠M.

20.

For each angle given below, write the name of the vertex, the names of the arms and the name of the angle.

Answer»

(i) In figure (i) O is the vertex, OA, OB is its arms and name of the angle is ∠AOB or∠BOA or simply ∠O.

(ii) In figure (ii) Q is the vertex, QP and QR its arms and the name of the angle is ∠PQR or ∠RQP or simply ∠Q.

(iii) In figure (iii), M is the vertex, MN and ML and its anus, and the name of the angle is ∠LMN or ∠NML or simply ∠M.

Discussion

21.	Find the angle between minute hand and the hour hand of a clock when the time is 5.40.
Answer» Angle described by the hour hand is 12 hours = 360° ∴ per hour = 360°/12 = 30° ∴ Angle described in 5 hour 40 minutes i.e., in 17/3 x 30° = 170° Now the angle described by minute hand is 60° minutes = 360° i.e., Angle in 40° minutes = 40 × 6° = 240°, ∴ Angle between the minutes hand to hour hand = 240° - 170° = 70° = (70° x π)/180 = 7π/18 radians

21.

Find the angle between minute hand and the hour hand of a clock when the time is 5.40.

Answer»

Angle described by the hour hand is 12 hours = 360°

∴ per hour = 360°/12 = 30°

∴ Angle described in 5 hour 40 minutes i.e., in 17/3 x 30° = 170°

Now the angle described by minute hand is 60° minutes = 360° i.e., Angle in 40° minutes = 40 × 6° = 240°,

∴ Angle between the minutes hand to hour hand = 240° - 170° = 70° = (70° x π)/180 = 7π/18 radians

Discussion

22.	Prove that tan α√(1 - sin2α) = sinα
Answer» LHS : tanα √(1 - sin2α) = tanα √cos²α = sinα/cosα x cosα = sinα = RHS

22.

Prove that tan α√(1 - sin2α) = sinα

Answer»

LHS : tanα √(1 - sin2α) = tanα √cos²α

= sinα/cosα x cosα = sinα = RHS

Discussion

23.	Express 25°. 30′ 10″ in radians.
Answer» 25° + (1/2)° + (1/6)° = (150 + 3 + 1)/6 = 154/6 = 77°/3 ⇒ 77/3 x π/180 = 77π/540 radians

23.

Express 25°. 30′ 10″ in radians.

Answer»

25° + (1/2)° + (1/6)° = (150 + 3 + 1)/6 = 154/6 = 77°/3

⇒ 77/3 x π/180 = 77π/540 radians

Discussion

24.	In the given figure, AOB is a straight line. Find the value of x and also answer each of the following :(i) ∠AOP = ……..(ii) ∠BOP = ……..(iii) which angle is obtuse ?(iv) which angle is acute ?
Answer» ∠AOP = x + 30° ∠BOP = x – 30° But ∠AOP + ∠BOP = 180° (∵ ∠AOB is a straight angle) ⇒ x + 30°+ x - 30° = 180° ⇒ 2x = 180° ⇒ x = 90° (i) ∠AOP = x + 30° = 90° + 30° = 120° (ii) ∠BOP = x- 30° = 90° – 30° = 60° (iii) ∠AOP is an obtuse angle (iv) ∠BOP is an acute angle

24.

In the given figure, AOB is a straight line. Find the value of x and also answer each of the following :(i) ∠AOP = ……..(ii) ∠BOP = ……..(iii) which angle is obtuse ?(iv) which angle is acute ?

Answer»

∠AOP = x + 30°

∠BOP = x – 30°

But ∠AOP + ∠BOP = 180° (∵ ∠AOB is a straight angle)

⇒ x + 30°+ x - 30° = 180°

⇒ 2x = 180°

⇒ x = 90°

(i) ∠AOP = x + 30° = 90° + 30° = 120°

(ii) ∠BOP = x- 30° = 90° – 30° = 60°

(iii) ∠AOP is an obtuse angle

(iv) ∠BOP is an acute angle

Discussion

25.	In the given figure ; AOC-is a straight line. If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of :(i) angle BOC(ii) angle EOD(iii) obtuse angle BOD(iv) reflex angle BOD(v) reflex angle COE.
Answer» (i) ∠AOB + ∠BOC = 180° (Linear pairs of angle) ⇒ 50° +∠BOC = 180° ⇒ ∠BOC = 180° – 50° = 130° ⇒ ∠BOC = 130° (ii) ∠EOD + ∠COD = 90° (∵AOE = 90°) ⇒ ∠EOD + 25° = 90° ⇒ ∠EOD + 25° = 90° ⇒ ∠EOD = 90° – 25° ⇒ ∠EOD = 65° (iii) ∠BOD = ∠BOC + COD = 130° + 25° = 155° (iv) Reflex ∠BOD = 360° – ∠BOD = 360°- 155° = 205° (v) Reflex ∠COE = 360° – ∠COE = 360° (∠COD + ∠EOD) = 360° – (25° + 65°) = 360° – 90° = 270°

25.

In the given figure ; AOC-is a straight line. If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of :(i) angle BOC(ii) angle EOD(iii) obtuse angle BOD(iv) reflex angle BOD(v) reflex angle COE.

Answer»

(i) ∠AOB + ∠BOC = 180° (Linear pairs of angle)

⇒ 50° +∠BOC = 180°

⇒ ∠BOC = 180° – 50° = 130°

⇒ ∠BOC = 130°

(ii) ∠EOD + ∠COD = 90° (∵AOE = 90°)

⇒ ∠EOD + 25° = 90°

⇒ ∠EOD = 90° – 25°

⇒ ∠EOD = 65°

(iii) ∠BOD = ∠BOC + COD

= 130° + 25° = 155°

(iv) Reflex ∠BOD = 360° – ∠BOD

= 360°- 155° = 205°

(v) Reflex ∠COE = 360° – ∠COE

= 360° (∠COD + ∠EOD)

= 360° – (25° + 65°)

= 360° – 90° = 270°

Discussion

26.	In the given figure if :(i) a = 130° ; find b.(ii) b = 200 ; find a.(iii) a = 5/3 right angle, find b
Answer» (i) From figure, a + b = 360° ⇒ 130° + 6 = 360 ⇒ 6 = 360°-130° ⇒ b = 230° (ii) From figure, a + b = 360° ⇒ a + 200° = 360° ⇒ a = 360° – 200° ⇒ a = 160° (iii) Here, a = 5/3 right angle = 5/3 x 90° = 150° a = 150° Here, a + b = 360° ⇒ 150° + b = 360° (∵a = 150°) ⇒ b = 360° -150° b = 210°

26.

In the given figure if :(i) a = 130° ; find b.(ii) b = 200 ; find a.(iii) a = 5/3 right angle, find b

Answer»

(i) From figure,

a + b = 360°

⇒ 130° + 6 = 360

⇒ 6 = 360°-130°

⇒ b = 230°

(ii) From figure,

a + b = 360°

⇒ a + 200° = 360°

⇒ a = 360° – 200°

⇒ a = 160°

(iii) Here, a = 5/3 right angle

= 5/3 x 90° = 150°

a = 150°

Here, a + b = 360°

⇒ 150° + b = 360° (∵a = 150°)

⇒ b = 360° -150°

b = 210°

Discussion

27.	If x = a cos θ + sin θ. y = a sin θ – b cos θ. Show that x2 + y2 = a2 + b2
Answer» Consider x² = (acosθ + bsin θ)² ⇒ x² = a²cos²θ + 2abcosθsinθ + b²sin²θ …….(1) Again consider y² = (asinθ – bcosθ)² ⇒ y² = a²sin²θ – abcosθ sinθ + b²cos²θ …….. (2) (1) + (2) ⇒ x² + y² = a² + b²

27.

If x = a cos θ + sin θ. y = a sin θ – b cos θ. Show that x2 + y2 = a2 + b2

Answer»

Consider x² = (acosθ + bsin θ)²

⇒ x² = a²cos²θ + 2abcosθsinθ + b²sin²θ …….(1)

Again consider y² = (asinθ – bcosθ)²

⇒ y² = a²sin²θ – abcosθ sinθ + b²cos²θ …….. (2)

(1) + (2) ⇒ x² + y² = a² + b²

Discussion

28.	Find the value of cos(π/3) – sin(π/6) – tan3(π/6)
Answer» Now cos(π/3) - sin(π/6) - tan³(π/4) = 1/2 - 1/2 - 1³- 1

28.

Find the value of cos(π/3) – sin(π/6) – tan3(π/6)

Answer»

Now cos(π/3) - sin(π/6) - tan³(π/4)

= 1/2 - 1/2 - 1³- 1

Discussion

Explore topic-wise InterviewSolutions in .

Name the points :(i) in the interior of the angle PQR,(ii) in the exterior of the angle PQR.

The measures of two supplementary angles are (3x + 15)° and (2x + 5)°. Find x.

In the given figure, PQR is a straight line. Find x. Then complete the following:(i) ∠AQB = ……..(ii) ∠BQP = ……..(iii) ∠AQR = …….

In the given diagram, ABC is a straight line.(i) If x = 53°, find y.(ii) If y =1 1/2 right angles ; find x.

Explain what do you understand by :(i) Adjacent angles ?(ii) Complementary angles ?(iii) Supplementary angles ?

Two complementary angles are in the ratio 7 : 8. Find the angles.

The measures of two complementary angles are (2x – 7)° and (x + 4)°. Find x.

For an angle x°, find :(i) the complementary angle(ii) the supplementary angle(iii) the value of x° if its supplementary angle is three times its complementary angle.

In the given figure; AB, CD and EF are straight lines. Name the pair of angles forming :(i) straight line angles.(ii) vertically opposite angles.

Example for obtuse angle.(1) 90°(2) 53°(3) 178°(4) 180°

Write the complement angle of :(i) 45°(ii) x°(iii) (x – 10)°(iv) 20° + y°

Give two examples of parallel lines you can see in your environment.

Give two examples of perpendicular lines you can see in your environment.

Match the following:Measure of theangleType of the anglei. 180°a. Zero angleii. 240°b. Straight angleiii. 360°c. Reflex angleiv. 0°d. Complete angle

Say, true or false of the following:i. Parallel lines do not intersect each other.ii. Pole and its shadow on the ground makes a cute angle.iii. Angle between two parallel lines is 90°.iv. Angle between two intersecting lines may or may not be 90°.

Complete the following table:AngleName of the angleVertex of the angleArts of the angle

Look at the pictures below and identify the different types of angles.

Look at the figures below and write the type of each of the angles:

Measure the angles given below and write the measure in the given blanks. ......... ........ ......... . ...... .

For each angle given below, write the name of the vertex, the names of the arms and the name of the angle.

Find the angle between minute hand and the hour hand of a clock when the time is 5.40.

Prove that tan α√(1 - sin2α) = sinα

Express 25°. 30′ 10″ in radians.

In the given figure, AOB is a straight line. Find the value of x and also answer each of the following :(i) ∠AOP = ……..(ii) ∠BOP = ……..(iii) which angle is obtuse ?(iv) which angle is acute ?

In the given figure ; AOC-is a straight line. If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of :(i) angle BOC(ii) angle EOD(iii) obtuse angle BOD(iv) reflex angle BOD(v) reflex angle COE.

In the given figure if :(i) a = 130° ; find b.(ii) b = 200 ; find a.(iii) a = 5/3 right angle, find b

If x = a cos θ + sin θ. y = a sin θ – b cos θ. Show that x2 + y2 = a2 + b2

Find the value of cos(π/3) – sin(π/6) – tan3(π/6)