Question

Question 3
An exterior angle of a triangle is ${105}^{\circ }$ and its two interior opposite angles are equal. Each of these equal angles is:

A) $37{\frac{1}{2}}^{\circ }$
B) $52{\frac{1}{2}}^{\circ }$
C) $72{\frac{1}{2}}^{\circ }$
D) ${75}^{\circ }$​​​​​​​

Answer 1

The answer is B.
Let one of interior angle be $x^{\circ }$.
$\because$ Sum of two opposite interior angles = Exterior angle
$\therefore x^{\circ }+x^{\circ }={105}^{\circ }$
$\Rightarrow 2x^{\circ }={105}^{\circ }$
$\therefore x^{\circ }=\frac{{105}^{\circ }}{2}$
$\Rightarrow x^{\circ }=52{\frac{1}{2}}^{\circ }$
Hence, each angle of a triangle is $52{\frac{1}{2}}^{\circ }$.