Question

An exterior angle of a triangle is 110° and the two interior opposite angles are equal.
Each of these angles is

(a) 70°

(b) 55°

(c) 35°

(d) 110°

Answer 1

Let $∆ABC$ be the triangle in which $\angle BCD={110}^{\circ }$ is the exterior triangle as shown in the figure.

Given: $\angle ABC=\angle BAC$
An exterior angle of a triangle is equal to the sum of the opposite interior angles, therefore

$$\begin{gathered} \angle ABC+\angle BAC=\angle BCD \\ \Rightarrow \angle ABC+\angle ABC={110}^{\circ }\left(\because \angle ABC=\angle BAC\right) \\ \Rightarrow 2\angle ABC={110}^{\circ } \\ \Rightarrow \angle ABC={55}^{\circ } \end{gathered}$$
Thus, the measure of the equal angles is ${55}^{\circ }$.
Hence, the correct option is (b).