Question

An exterior angle of a triangle is $105°$ and its two interior opposite angles are equal. Each of these equal angle is

• A. $37{\frac{1}{7}}^{\circ }$
• B. $52{\frac{1}{2}}^{\circ }$
• C. $72{\frac{1}{2}}^{\circ }$
• D. $75°$

Answer 1

The correct option is B

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

Explanation for the Correct option:

Finding the value of the interior angle:.

Let one of the interior angles be $x^{\circ }$
Since, the sum of two opposite interior angles = Exterior angle
$\therefore x°+x°=105°(\because \text{interior angles are equal})$

$\Rightarrow$ $2x°=105°$
$\Rightarrow$ $x°=\frac{{105}^{\circ }}{2}$
$\Rightarrow$ $x°=52{\frac{1}{2}}^{\circ }$

Therefore, the measure of each of the opposite interior angles, $x°=52{\frac{1}{2}}^{\circ }$.

Hence, option (B) is the correct answer.