Question

In the triangle ABC, AB = AC and $\angle A:\angle B=8:5$. Then $\angle A$ equals

• A. ${40}^{\circ }$
• B. ${50}^{\circ }$
• C. ${60}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is D

${80}^{\circ }$

Let $\angle A=8x$ and $\angle B=5x$

Given AB = AC

$⟹\angle B=\angle C=5x$ (angles opposite to equals sides are equal)

Now, $\angle A+\angle B+\angle C={180}^{\circ }$

$⟹8x+5x+5x={180}^{\circ }$

$⟹x={10}^{\circ }$

Given, $\angle A=8x$

Then $\angle A=8\times {10}^{\circ }={80}^{\circ }$