Question

The vertical angle of an isoceles triangle is three time the sum of its base angles. Find all the angles of the triangle.

Answer 1

In $\Delta ABC$
AB = AC

$\angle A=3(\angle B+\angle C)$
Let $\angle B=x$
$\therefore \angle C=x$
$\therefore \angle B+\angle C=2x,Hence\angle A=3x$
Thus by angle sum property
$2x+3x=180$
$5x=180$
$x=\frac{180}{5}$
Thus, $\angle C=\angle B=\frac{180}{5}$ = ${36}^{\circ }$
Angle A = ${108}^{\circ }$