Question

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

• A. $37{\frac{1}{2}}^o$
• B. $52{\frac{1}{2}}^o$
• C. $72{\frac{1}{2}}^o$
• D. ${75}^o$

Answer 1

Answer: (B)

$52{\frac{1}{2}}^o$

By exterior angle theorem,
Exterior angle = Sum of interior opposite angles
Let each interior opposite angles = $x$
$105=x+x$
$105=2x$
$x=52{\frac{1}{2}}^{\circ }$.