Question

Suppose that △ OPQ is isosceles with base QP . Suppose also that m ∠ O = (5x + 43) ° and m ∠ Q = (3x + 30) ° . Find the degree measure of each angle in the triangle.

Answer 1

Measure of O: 78 degrees

Measure of Q: 51 degrees

Measure of P: 51 degrees

Explanation:

If it has base QP, then angles Q and P are equal, so we now have the measure of angle P: It is the same as Q! This is also 3x + 30, so now we have 5x + 43 + 3x + 30 + 3x + 30 = 180, or 11x + 103 = 180, so 11x = 77, and x = 7. Plug these back in to get O = 78, Q = 51, and P is 51.