Question

If ABC is a triangle and ∠BCD is an exterior angle then, the measure of ∠BCD is equal to:

1. is equal to twice of ∠A

2. the sum of all three interior angles of ΔABC

3. the sum of interior opposite angles of ∠BCD

4. the sum of ∠B and adjacent angle of ∠BCD

Answer 1

The measure of the exterior angle ∠BCD in a triangle ABC is equal to twice the measure of angle A.

The correct answer to the given question is option 1.

The measure of the exterior angle ∠BCD in a triangle ABC is equal to twice the measure of angle A.

This is known as the Exterior Angle Theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

In this case, ∠BCD is an exterior angle, and the non-adjacent interior angles are ∠A and ∠BCD, so ∠BCD = ∠A + ∠BCD. Rearranging the equation, we have ∠BCD = ∠A * 2.