Find the measures of all three angles in an isosceles triangle if the ratio between the base angles and the vertex angle is 3 to 2 respectively.

Question

the measures of all three angles in an isosceles triangle if the ratio between the base angles and the vertex angle is 3 to 2 respectively.

Answer 1

If vertex angle is 2x, then base angles are 3x each

Since sum of angles of a triangle are 180, then

2x + 3x + 3x = 180

8x = 180

x = 22.5

2x = 45

3x = 67.5

vertex angle is 45 degrees, base angles are 67.5 degrees