One of the exterior angles of a triangle is 80°, and the interior opp

1.	One of the exterior angles of a triangle is 80°, and the interior opposite angles are equal to each other. What is the measure of each of these two angles?
Answer» Let us assume that A and B are the two interior opposite angles. We know that ∠A is equal to ∠B. We also know that the sum of interior opposite angles is equal to the exterior angle. Therefore from the figure we have, ∠A + ∠B = 80° ∠A +∠A = 80° (because ∠A = ∠B) 2∠A = 80° ∠A = 40/2 =40° ∠A= ∠B = 40° Thus, each of the required angles is of 40°.

One of the exterior angles of a triangle is 80°, and the interior opposite angles are equal to each other. What is the measure of each of these two angles?

Answer»

Let us assume that A and B are the two interior opposite angles.

We know that ∠A is equal to ∠B.

We also know that the sum of interior opposite angles is equal to the exterior angle.

Therefore from the figure we have,

∠A + ∠B = 80°

∠A +∠A = 80° (because ∠A = ∠B)

2∠A = 80°

∠A = 40/2 =40°

∠A= ∠B = 40°

Thus, each of the required angles is of 40°.