Question

An exterior angle of a triangle is 105° and it's two interior opposite angles are equal. find each of these equal angles

A)
$37 \times \frac{1}{2}$
​

Answer 1

Answer:

52.5°

Step-by-step explanation:

Let the two equal interior angles be a and a.

Third angle makes a linear pair with 105°. So their sum should be 180°.

= > third angle + 105° = 180°

= > third angle = 180° - 105° = 75°

In any triangle, sum of all angles is 180°.

Here,

= > a + a + 75° = 180°

= > 2a = 180° - 75°

= > 2a = 105°

= > a = (105/2)° = 52.5°

Measure of equal angles is 52.5°