Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

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