Each face of a pyramid is an isosceles triangle with a 62 degree vertex angle. What are the measures of the base angles? The measures of the base angles are ?

180° - 62° = 118°          118° ÷ 2 = 59°

This is the measure of each of the two base angles.

Step-by-step explanation:

Each face of a given pyramid is an isosceles triangle, with a 62° vertex angle.

Recall that an isosceles triangle has only 1 vertex angle.

- An isosceles triangle is one with 2 equal sides. Recall the Base Angle Theorem which states that in an isosceles triangle, the congruent sides have or produce congruent angles. This results in 2 equal base angles, in the regular case.

- The third angle is the vertex angle.

- To derive base angles from a vertex angle, subtract the value of the vertex angle from 180°. Divide the answer you get by 2. This is the value of each base angle.

- Remember also; the sum of all angles in a triangle must = 180°

180° - 62° = 118°          118° ÷ 2 = 59°

This is the measure of each of the two base angles.