Explore topic-wise InterviewSolutions in .

The correct option is (a) True

Easy explanation: RECTANGLES are four sided closed polygons with OPPOSITE sides equal and parallel to each other, but square is a POLYGON with all sides equal and opposite sides parallel. THEREFORE the given STATEMENT is true and square are considered to be special cases i.e. rectangles with all sides equal.

Correct option is (a) SAS

For explanation: The triangle formed by a side of a rectangle and the DIAGONALS have,

(i) Side 1 (DIAGONAL)

(ii) ANGLE (vertically opposite angle)

(iii) Side 2 (diagonal)

Hence the TRIANGLES are similar by SAS test of similarity.

Right choice is (a) RECTANGLE

To EXPLAIN: A rectangle has it’s opposite sides equal and all angles are right angles, if all the sides are equal then this figure FULFILLS all the properties of a SQUARE. HENCE a square is a rectangle with all sides equal.

The correct choice is (a) True

The explanation is: As we know that rhombus is a special type of polygon where all the angles measure ACUTE angle and all the sides of the polygon are EQUAL in LENGTH. The DIAGONALS of rhombus have the property that they are perpendicular bisectors of each other i.e. they meet each other at RIGHT angle and bisect each other.

Correct CHOICE is (a) TRUE

The best EXPLANATION: The given STATEMENT is true. Rhombus has all the properties of a parallelogram and that of any kite.

The CORRECT option is (b) perpendicular BISECTOR of each other

For explanation I would say: As we know that rhombus is a special type of polygon where all the angles MEASURE ACUTE angle and all the sides of the polygon are equal in length. The diagonals of rhombus have the property that they are perpendicular bisectors of each other i.e. they meet each other at right angle and bisect each other.

The correct choice is (a) equal

The BEST I can explain: As we know that rhombus is a special TYPE of polygon where all the angles measure ACUTE angle and all the sides of the polygon are equal in LENGTH.

The correct option is (b) False

The best explanation: The sum of internal angle of a three-sided polygon is 180° and that of a QUADRANGLE is 360°; because a quadrangle can be SPLIT into TWO triangles and we KNOW that the sum of interior angles of the TRIANGLE is 180. So, two times 180 is 360.

Correct CHOICE is (a) False

Easiest explanation: Quadrangles as the word suggest are four SIDED polygon. The word quadrangle is split as ‘Quadra’ meaning four, so a quadrangle has four angles and four SIDES.

Right OPTION is (b) False

Explanation: A triangle with INTERNAL acute angle is not always an equilateral triangle. But, an equilateral triangle has equal acute angle. In the given FIGURE, the SIDES of the triangle are not equal, but it has acute interior angles.

The correct option is (B) False

Easy explanation: A three-sided polygon is called a triangle. If all the three sides are equal then it is called an EQUILATERAL triangle. If TWO sides of a triangle are equal then it is an ISOSCELES triangle.

Correct answer is (d) Curve of the shape

The EXPLANATION is: The number of sides, its angle between the sides and the LENGTH of the sides decide the TYPE and shape of the polygon. For, a PENTAGON has five sides and internal angle of 108°.

Right option is (a) True

To ELABORATE: A polygon is a two-dimensional figure with STRAIGHT sides. CIRCLES and other CURVE cannot be TERMED as polygon as they have no straight sides. Here, in the given figure the trapezium has two parallel sides and two straight lines.

Right answer is (a) True

To elaborate: An APOTHEM is a LINE from the center of the regular polygon at right ANGLES to any of its sides.This line is ALSO the radius of the incircle. Hence, an apothem is the radius of the incircle of a regular polygon.In the given FIGURE, the line AB is the apothem of the polygon as well as the radius of the incircle.

Right answer is (a) 360°

For explanation I WOULD say: The sum of the external ANGLES of a regular polygon is always 360°. When we push all the angles of a convex polygon the angle CONVERGES and form a TOTAL of 360°. This angle is also called as perigon angle.

The correct option is (a) False

To EXPLAIN I would say: A CIRCLE INSCRIBED in a polygon is CALLED an incircle (in meaning inside). A circle circumscribing the polygon, or just touching the vertices of the polygon is called as circumcircle.

Right answer is (c) Pentacontagon

To elaborate: A POLYGON with fifty sides is called as pentacontagon. The SUM of the INTERIOR ANGLES of a pentacontagon is 8640° and the EXTERIOR angle of a pentacontagon is 7.2°.

The CORRECT ANSWER is (d) Circumcircle

Explanation: A circle which connects all the vertices of the TRIANGLE is CALLED as a circumcircle. Whereas, if touches the sides of the polygon internally then it is called as incircle.

Correct ANSWER is (b) 60°

Easy EXPLANATION: The exterior angles of a POLYGON can be found USING the formula = \(\frac{360}{NUMBER \, of \,sides}\).

Since, the number of sides of a hexagon is 6.

Therefore, the exterior angle of a hexagon is = \(\frac{360}{6}\) = 60°

The correct choice is (b) False

Explanation: A polygon is a shape constructed USING STRAIGHT SIDES. It is encompassed WITHIN the boundaries of lines in a regular or irregular manner. But a circle or any other curve does not fall under polygon. It is two dimensional in NATURE.

The CORRECT option is (C) LENGTH

The explanation is: The length of the polygon can be used to find the perimeter and area of a polygon. Since, the perimeter and area are in relation with the sides of the polygon, THEREFORE they PLAY a major role in finding the two parameters.

The CORRECT choice is (d) 900

To ELABORATE: The sum of the interior ANGLES of a polygon can be calculated using the formula = (number of sides – 2) × 180

Here, number of sides is 7.

So, the sum of interior angles of a septagon = (7 – 2) × 180 = 5 × 180 = 900

Right CHOICE is (a) Isosceles

The explanation: As we KNOW that there are three types of triangle

(i) Equilateral Triangle: All sides are EQUAL in LENGTH and all the angles measure 60°

(ii) Isosceles Triangle: Two sides are of equal length and the corresponding BASE angles would be of equal measure.

(iii) Scalene Triangle: All three sides of the different lengths and all the angles are of different measures.

Right choice is (d) CIRCLE

For EXPLANATION I would say: Circle is not considered to be a polygon because it is a closed curve WHEREAS the definition SAYS that a ‘n’ sided closed FIGURED containing straight lines is known as polygon. Since the circle does not satisfy all the conditions for a polygon it is not considered as a polygon.

The CORRECT answer is (a) Rectangle

Easy explanation: When the set square are PLACED along their hypotenuse they form a rectangle. The set squares WOULD look LIKE the below figure. On the contrary if the set squares are of MEASURE 45°-45°-90°, then the polygon formed is square.

Correct option is (b) Square

Best EXPLANATION: In a parallelogram all the SIDES are of equal length and the opposite sides are parallel to each other. This all conditions are satisfied by square and since all the ANGLES MEASURE 90°, therefore it is considered as the special case of parallelogram.

The correct choice is (b) ISOSCELES trapezium

Easiest explanation: If the TWO non-parallel SIDES of the trapezium are equal in length then the trapezium is known as Isosceles Trapezium. This is a SPECIAL TYPE of trapezium.

Correct ANSWER is (C) adjacent

For explanation I would say: Kite is a special type of polygon in which the CONSECUTIVE (adjacent) sides of the figure are equal in LENGTH and the diagonals are PERPENDICULAR but only one of them bisects the other. Therefore here the correct answer would be adjacent.

The correct answer is (c) 3

Best explanation: If a student has three identical cutting of a right ANGLED TRIANGLE and PLACES it in a specific manner then the formation FORMED with these triangles is KNOWN as trapezium. So, here Raj can give three triangles to his friends.

The CORRECT answer is (B) False

To explain: Each EXTERIOR angle of any N-sided polygon=(360°)/n

If the exterior angle is 70°,

Then (360°)/n = 70

Therefore n=5.1. Here ‘n’ is the number of sides and since the number of sides cannot be any decimal number the answer to the statement is false.

Right OPTION is (b) 2

For explanation: A polygon which has it’s one pair of opposite sides parallel to each other is KNOWN as trapezium. So the number of sides parallel would be 2. The option which states that all the sides are parallel can be straight away ruled out because if all the sides are parallel it won’t be FORMING a closed FIGURE.

Correct answer is (a) True

To EXPLAIN I would say: External angle of any polygon can be seen when the SIDE of the polygon is extended and HENCE the external angle and the internal angle form a pair of linear angle. The sum of these two angles is ALWAYS EQUAL to 180°. They are also known as straight angles.

Correct OPTION is (a) 170/2°

Easiest explanation: Here we will USE the property of EXTERNAL angles.

Therefore (x-10)°+x=180°

Therefore x-10+x=180°

Therefore 2x=170

Therefore x=170/2.

The CORRECT choice is (d) 360°

The best I can explain: As we know from our prior KNOWLEDGE that all the angles in any EQUILATERAL triangle the angles measure 60°. Therefore the external ANGLE would be measuring 120° as the pair of internal and external angles is ALWAYS linear. Since there are three identical external angles, therefore our answer would be 120 ×3=360°.

The correct OPTION is (c) 140/3

Easiest explanation: Here we are GIVEN a TRIANGLE with all it’s internal angles marked in terms of x.

Now we will use the PROPERTY of triangle.

Therefore (x+20)°+(x+30)°+(x-10)°=180°

Therefore x+20+x+30+x-10=180

Therefore 3x=140

Therefore x=140/3.

Correct choice is (a) 160°

Easy EXPLANATION: As we know that sum of all the internal angles of the TRIANGLE is 180°.

Therefore x+y+z=180°

Therefore 30°+130°+z=180°

Therefore z=120°

Now we know that the external angle is ALWAYS a LINEAR angle.

Therefore x+y=180°

Therefore 20°+y=180°

Therefore y=160°.

Right option is (a) 90°

The best explanation: We know that the rectangle has all it’s angle as 90°. All the external angles MAKE straight angle with the internal angles. Therefore all the angles WOULD be 90°. The information provided about the perimeter is of no USE.

The correct answer is (d) 360°

Explanation: As we know that the external angles for a supplementary pair of angles with the internal angles. We TAKE any square of any LENGTH, as we know that all the angles of a square MEASURE 90° and we ALSO know that they are supplementary.

Therefore 90°+x = 180°

Therefore x = 90°

Similarly the other THREE external angles also measure the same. Therefore the sum total of all the external angles is 360°.

Right option is (c) The angles forming a pair of supplementary angles

For explanation I would say: If an extended ray along a SIDE of a polygon form a linear pair with the same side of the polygon then the angle MADE by the polygon and the extended ray is said to be exterior angle of that polygon. Any polygon having ‘n’ NUMBER of SIDES the sum of all EXTERNAL angels is 360°.

The CORRECT answer is (b) False

Explanation: The formula (n-2)180° is the formula for the interior ANGLES of the polygon.

As we know the sum ANGLE property of the SQUARE is 360°.

Therefore (n-2)180°

Therefore (4-2)180°

Therefore 360°.

Right choice is (d) Three angles

Best explanation: In any triangle irrespective of any type of triangle it has three angles in total. Here if the question WOULD ask the ‘how MANY angles other than right ANGLE’ then the ANSWER would be two angles.

Right answer is (d) 60°, 30° and 90°

Easy EXPLANATION: In a scalene triangle the measure of all the ANGLES and the SIDES is different. The options other then 60°, 30° and 90° are either equilateral triangles or isosceles triangles.

Right option is (c) 180°

Explanation: A circle SUBTENDS a whole of 360°, this is the measure of one complete ROTATION over the circumference of the circle. Now, the semicircle WOULD SUBTEND an angle of 180°.

The correct CHOICE is (c) 20°

For explanation: One can get the hint that the given triangle is isosceles triangle by OBSERVING the length of all the sides. As in an isosceles triangle two sides are of equal length and also the base ANGLES are equal in measure. Let the apex angle for denoted by the variable x.

Therefore 80+80+x=180

Therefore 160+x=180

Therefore x=20.