Find the measures of the angles of an isosceles triangle where the ratio of the vertex angle to one of the base angles is 1:2.

Answer 1

If the vertex angle is x, then the base angle is 2x. Since the base angles of an isosceles triangle are equal, the other base angle is 2x.

The sum of the angles of a triangle are 180 so: x + 2x + 2x = 180 and x = 36 and 2x = 72.

Thus, the vertex angle is 36 degrees and the two base angles are 72 degrees each.