Question

Each of the two equal angles of a triangle is twice the third angle. Find the angles of the triangle.

Answer 1

Let third angle be $x$

Therefore, two equal angles are $2x$ and $2x$.

Now, we know that sum of angles of three angles of a triangle is ${180}^{\circ }$.

$\Rightarrow x+2x+2x={180}^{\circ }$

$\Rightarrow 5x={180}^{\circ }$

$\Rightarrow x={36}^{\circ }$

Hence, the three angles of the triangle are,

Third angle $={36}^{\circ }$

Second angle $={72}^{\circ }$

First angle $={72}^{\circ }$