Question

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?
(3 marks)

Answer 1

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

We know that $\angle A$ is equal to $\angle B.$

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

Therefore, we have,

$\angle A+\angle B=80°$

(1 mark)

$\angle A+\angle A=80°$ (because $\angle A=\angle B$)

$2\angle A=80°$

$\angle A=\frac{80}{2}=40°$

(1 mark)

$\angle A=\angle B=40°$

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

(1 mark)