Question

an exterior angle of triangle is 110 and one of interior opposite angle is 30. find other two angles of triangles?

Answer 1

Let the ABC is the triangle and Exterior angle lies on Point A

Given that Exterior angle = 110°

One of its opposite interior angle (∠B) = 30°

∵ Exterior angle lies on point A ∴ opposite interior angles will be ∠B and ∠C

We know that

Exterior Angle = Sum of Opposite interior Angles

∴ ∠B + ∠C = 110°

30° + ∠C = 110°

∠C = 80°

Now

∠A + ∠B + ∠C = 180° (Angle Sum Property of Triangle)

∠A + 110° = 180°

∠A = 70°

∴ other two angle of the triangle are 70° and 80°

Answer 2

PQR is a Triangle [i.e. ∆PQR]

∠a + 110° = 180° 【Linear Pair】

⇒ ∠a = 180° - 110°
⇒ ∠a = 70°

∴∠a = ∠R = 70°

【Sum of all ∠s of ∆ = 180°】

∠P + ∠Q + ∠R = 180°

⇒ ∠P + 30° + 70° = 180°
⇒ ∠P + 100° = 180°
⇒ ∠P = 180° - 100°
⇒ ∠P = 80°

∴ ∠P = 80°

Hence, the other two angles are 70° and 80°.

Hope it helps ツ