Question

In the given isosceles triangle ABC, AB = AC, $\angle ABC$ = 70°. Find $\angle$ BAC.

• A. ${45}^{\circ }$
• B. ${50}^{\circ }$
• C. ${60}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is D

${40}^{\circ }$

Since ABC is an isosceles triangle, two sides of the triangle will be equal.
From the question, AB = AC

Hence, the base angles will be equal.
$\Rightarrow$ $\angle ABC$ = $\angle ACB$ = ${70}^{\circ }$

$\angle BAC$ + $\angle ABC$ + $\angle ACB$ = ${180}^{\circ }$ ( Angle sum property of a triangle)
$\Rightarrow \angle BAC+70°+70°=180°$
$\Rightarrow \angle BAC$ = ${180}^{\circ }$ - ${70}^{\circ }$ - ${70}^{\circ }$
$\Rightarrow \angle BAC$ = ${180}^{\circ }$ - ${140}^{\circ }$
$\Rightarrow \angle BAC$ = ${40}^{\circ }$

Hence, the value of $\angle BAC$ = 40°.