Question

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

[3 Marks]

Answer 1

Let ABC be a triangle whose side BC is produced to form an exterior angle ACD such that exterior ∠ACD = 110° [1 Mark]

Let ∠B = 30°. By exterior angle theorem, we have ext. ∠ACD = ∠B + ∠A

⇒ 110° = 30° + ∠A
⇒ ∠A = 110° – 30°
⇒ ∠A = 80° [1 Mark]

In ΔABC, we have
∠A + ∠B + ∠C = 180°
⇒ 80° + 30° + ∠C = 180°
⇒ ∠C = 180° – 80° – 30°
⇒ ∠C = 180° – 110°
⇒ ∠C = 70°

Therefore, the other two angles of the triangle are 80° and 70°. [1 Mark]