Find, giving reasons, the unknown marked angles, in each triangle draw

1.	Find, giving reasons, the unknown marked angles, in each triangle drawn below:
Answer» We know that, Exterior angle of a triangle is always equal to the sum of its two interior opposite angles (property) (i) ∴ 110° = x + 30° (by property) ⇒ x =110°- 30° x = 80° (ii) x + 115° = 180° (linear property of angles) ⇒x = 180°- 115° ⇒x = 65° ∴115° = x + y ⇒ 115° = 65° + y ⇒ y= 115° – 65° = 50° y = 50° (iii) 110° = 2x + 3x 5x – 110° x = (110/5) ° x = 22° ∴ 2x = 2 x 22 = 44° 3x = 3 x 22 = 66°

Find, giving reasons, the unknown marked angles, in each triangle drawn below:

Answer»

We know that,

Exterior angle of a triangle is always equal to the sum of its two interior opposite angles (property)

(i) ∴ 110° = x + 30° (by property)

⇒ x =110°- 30° x = 80°

(ii) x + 115° = 180°

(linear property of angles)

⇒x = 180°- 115° ⇒x = 65°

∴115° = x + y

⇒ 115° = 65° + y

⇒ y= 115° – 65° = 50°

y = 50°

(iii) 110° = 2x + 3x

5x – 110°

x = (110/5) °

x = 22°

∴ 2x = 2 x 22 = 44°

3x = 3 x 22 = 66°