Question

Question 121

Each of the two equal angles of an isosceles triangle is four times the third angle. Find the angles of the triangle.

Answer 1

Let the third angle be x. Then, the other two angles are 4x and 4x, respectively.

We know that, the sum of all three angles in a triangle is ${180}^{\circ }$ i.e. $\angle A+\angle B+\angle C={180}^{\circ }$
$\Rightarrow x+4x+4x={180}^{\circ }\Rightarrow 9x={180}^{\circ }\Rightarrow x=\frac{{180}^{\circ }}{9}={20}^{\circ }$
Hence, the three angles are $4x=4\times {20}^{\circ }={80}^{\circ },4x=4\times {20}^{\circ }={80}^{\circ }$ and $x={20}^{\circ }$