Question

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

• A. 37.5${}^{\circ }$
• B. 52.5${}^{\circ }$
• C. 72.5${}^{\circ }$
• D. 75${}^{\circ }$

Answer 1

The correct option is B

52.5${}^{\circ }$

From the properties of triangles:

Exterior angle = Sum of interior opposite angles

Now let us take each interior opposite angle as x ( as both interior opposite angles are equal)

⇒ x + x = 105${}^{\circ }$

⇒ 2x = 105${}^{\circ }$

⇒ x = 52.5${}^{\circ }$

So the value of each of the opposite interior angle = 52.5${}^{\circ }$