Question

If an exterior angle of a triangle is 115° and one of the interior opposite angles is 35°, then the other two angles of the triangle are:

• A. 65°, 70°
• B. 45°, 60°
• C. 115°, 60°
• D. 65°, 80°

Answer 1

The correct option is D 65°, 80°



∠ACE=${115}^{\circ }$ and ∠A=${35}^{\circ }$

∠ACE=∠A+∠B (Exterior angle is equal to sum of interior opposite angles)

⇒${115}^{\circ }$ =${35}^{\circ }$+∠B

⇒∠B=${80}^{\circ }$

In ΔABC,

∠A+∠B+∠C=${180}^{\circ }$ (Angle sum property)

⇒${35}^{\circ }$+${80}^{\circ }$+∠C = ${180}^{\circ }$

⇒${115}^{\circ }$ + ∠C = ${180}^{\circ }$

⇒ ∠C = ${65}^{\circ }$

Hence, the other two angles are ${80}^{\circ }$​ and ${65}^{\circ }$.