The measure of a base angel of an isosceles triangle is 13 more than 3 times the measure of the vertex angel. How many degrees are in the vertex angel

Answer 1

Let x be the measure of the vertex angle.

According to the given information, the base angles are equal in an isosceles triangle. Therefore, each base angle is (3x + 13) degrees.

Since the sum of the angles in a triangle is 180 degrees, we can set up the following equation:

x + (3x + 13) + (3x + 13) = 180
7x + 26 = 180
7x = 154
x = 22

Therefore, the measure of the vertex angle is 22 degrees.