Question

An exterior angle of a triangle is ${120}^o$ and one of the interior opposite angles is ${30}^o$. Find the other angles of the triangle.

Answer 1

Let $X$ be other interior opposite angle of a $△XYZ$.

Let $Y$ be the third angle.

Exterior angle is equal to sum of interior opposite angles.

${120}^o={30}^o+\angle X$

$\Rightarrow \angle X={90}^o$

Now, Sum of interior angles of a triangle is ${180}^o$

$\Rightarrow {90}^o+{30}^o+\angle Y={180}^o$

$\Rightarrow \angle Y={180}^o-{120}^o={60}^o$