Question

Question 26

If the exterior angle of a triangle is ${130}^{\circ }$ and its interior opposite angles are equal, then measure of each interior opposite angle is

a) ${55}^{\circ }$
b) ${65}^{\circ }$
c) ${50}^{\circ }$
d) ${60}^{\circ }$

Answer 1

As we know, the measure of any exterior angle is equal to the sum of two opposite interior angles.
Let the interior angle be x.
Given that, interior opposite angles are equal.
$\therefore {130}^{\circ }=x+x$
$\Rightarrow {130}^{\circ }=2x\Rightarrow x=\frac{{130}^{\circ }}{2}\Rightarrow x={65}^{\circ }$
Hence, the interior angle is $={65}^{\circ }$