Question

An exterior angle of a triangle is equal to $100$ degrees and two interior opposite angles are equal. Each of these angles is equal to :

• A. ${75}^{\circ }$
• B. ${40}^{\circ }$
• C. ${80}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is D

${50}^{\circ }$

Given data:

1. The exterior angle of a triangle is ${100}^{\circ }$
2. The two interior opposite angles are equal.

Now we know that;

1. The exterior angle property of a triangle, states that the sum of two opposite (non-adjacent) interior angles is equal to the exterior angle.
2. The sum of two opposite equal interior angles is ${100}^{\circ }$.
3. Since, both the interior angles are equal, therefore each angle will be equal to $\frac{{100}^o}{2}={50}^o$.

Hence, the correct option is (D).