Question

The vertical angle in an isosceles triangle is ${80}^{\circ }$. Find its base angles.

• A. 55°
• B. 50°
• C. 75°
• D. 85°

Answer 1

The correct option is B (${50}^{\circ }$)

Let $\Delta ABC$ be an isosceles triangle with vertical angle $\angle A={80}^{\circ }$ and $AB=AC$
So, $\angle B=\angle C$
Since, the sum of three angles in a triangle is equal to ${180}^{\circ }$
Thus, $\angle A+\angle B+\angle C={180}^{\circ }$
$\Rightarrow {80}^{\circ }+\angle B+\angle B={180}^{\circ }$
$\Rightarrow 2\angle B={180}^{\circ }-{80}^{\circ }$
$\Rightarrow 2\angle B={100}^{\circ }$
$\Rightarrow \angle B=\frac{{100}^{\circ }}{2}$
$\therefore \angle B={50}^{\circ }$
Therefore, each base angle is ${50}^{\circ }$