Question

Consider the triangle below.

Determine the angle measure for angle A and angle M in order for triangle GAM to be classified as an isosceles triangle.

Answer 1

Given :

▪︎Measure of ∠G = 64°

▪︎△GAM is an isosceles triangle.

We know that :

▪︎The opposite base angles of an isosceles triangle are always equal.

Let the measure of ∠A be x.

Then, the measure of ∠M will also be x.

Which means :

`= \tt64 + x + x = 180`

`= \tt64 + 2x = 180`

`= \tt2x = 180 - 64`

`=\tt 2x = 116`

`=\tt x = (116)/(2)`

`= \tt \: x = 58`

Since the sum of all these angles is equivalent to 180°[64+58+58=180], we can conclude that we have found out the correct measure of each of these angles.

▪︎Therefore :

Measure of ∠A = 58°

Measure of ∠M = 58°