Question

The exterior angles, obtained on producing the side of a triangle both ways, are 100° and 120°. Find all the angles of the triangle.

Answer 1

∠ABP + ∠ABC = 180°    ....(Linear pair)
⇒ 100° + ∠ABC = 180°
⇒ ∠ABC = 180° - 100° = 80°

∠ACQ + ∠ACB = 180°   ....(Linear pair)
⇒ 120° + ∠ACB = 180°
⇒ ∠ACB = 180° - 120° = 60°

Now, in ΔABC,
∠A + ∠B + ∠C = 180°    ....(Angle sum property of a triangle)
⇒ ∠A + 80° + 60° = 180°
⇒ ∠A = 180° - 80° - 60° = 40°
Hence, the angles of a triangle are 40°, 60° and 80°.