Question

In each of the following figures,one side of a triangle has been produced.Find all the angles of the triangle in each case.​

Answer 1

Answer:

The Exterior angle Property of a triangle states that the sum of the two interior opposite angles of the triangle equals to the exterior angle.

(i) 50° + x° = 125°  (Exterior Angle Property)

x° = 125° - 50°

x = 75°

∠C = z°

z° + 125° = 180° (Linear Pair)

z° = 180° - 125°

z° = 55°

Hence ∠A = 50°

∠B = 75°

∠C = 55°

(ii) 2x ° + 3x° = 80° (Exterior Angle Property)

5x° = 80°

x° = 80° ÷ 5

x° = 16°

Hence ∠B = 2x

= 2 × 16

= 32°

∠C = 3x

= 3 × 16

= 48°

∠A = y

y + 80° = 180° (Linear Pair)

y = 180° - 80°

y = 100°

Ans is ∠B = 32°

∠C = 48°

∠A = 100°

(iii) y + 125° = 180° (Linear Pair)

y = 180° - 125°

y = 55°

55° + x = 125° (Exterior Angle Property)

x = 125° - 55°

x = 70°

Hence ∠A = 70°

∠B = 55°

∠C = 55°

Hope it helps