Question

An exterior angle of a triangle is 110° and one of the interior opposite angle is 30°.find the other two angles of the triangle.

Answer 1

We know that the sum of the two interior angles of a triangle is equal to the opposite exterior angle.
One of the angles is 30°
The exterior angle is 110°
Let the other unknown angle be = x
30°+ x = 110°
x = 110°-30°
x=80°
The other angle of the triangle is 80°.

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Answer 2

In the diagram, PQR is a Triangle.

∴ ∠a + 110° = 180° ❪Linear pair❫

⇒ ∠a = 180° - 110°

⇒ ∠a = 70°

Hence, ∠a = 70°.

∴ ∠P + ∠Q + ∠R = 180°

❪Sum of ∠s of a Triangle = 180°❫

⇒ ∠P + 30° + ∠a = 180°

⇒ ∠P + 30° + 70° = 180°

⇒ ∠P + 100° = 180°

⇒ ∠P = 180° - 100°

⇒ ∠P = 80°

Hence, ∠P = 80°.

Therefore, the other two angles of the triangle are 70° and 80°.

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