Question

In an isosceles triangle, a base angle is four times its vertical angle. Find all the angles of the triangle.

Answer 1

AB = AC
So,$\angle ABC=\angle ACB(\angle B=\angle C)$
Vertical angle = $\angle BAC$
According to question;
$\angle ABC=4\angle BAC(\angle B=4\angle A)$
$\therefore \angle A+\angle B+\angle C={180}^{\circ }$
$\angle A+2\angle B={180}^{\circ }$
$\angle A+8\angle A={180}^{\circ }$
$9\angle A={180}^{\circ }$
$\angle A={20}^{\circ }$
So, $\angle B=4\angle A={80}^{\circ }$
$\angle C={80}^{\circ }$
$\therefore \angle A,\angle B,\angle Care{20}^{\circ },{80}^{\circ }and{80}^{\circ }$.