The ratio of the measure of the vertex angle to the base angle of an isosceles triangle is 8 : 5. Find the measure of the vertex angle. Question 11Select one:a.b.c.d.

In an isosceles triangle, the base angles are equal and the sum of the angles in a triangle is 180 degrees.

Given that the ratio of the vertex angle to the base angle is 8:5, let's denote the measure of the base angle as 5x and the vertex angle as 8x.

Since the base angles are equal, the sum of the base angles is 2 * 5x = 10x.

The sum of all angles in the triangle is therefore 10x (sum of base angles) + 8x (vertex angle) = 180 degrees.

This gives us 18x = 180.

Solving for x, we get x = 180 / 18 = 10.

Substituting x = 10 into the expression for the vertex angle (8x), we get the measure of the vertex angle as 8 * 10 = 80 degrees.

So, the measure of the vertex angle is 80 degrees.