Geometry If △ABC is an isosceles triangle where AB¯¯≅AC¯¯ m∠A=(2x−20)°, and m∠B=(3x+5)°, then m∠C=__________°.

Question

If △ABC is an isosceles triangle where AB¯¯≅AC¯¯ m∠A=(2x−20)°, and m∠B=(3x+5)°, then m∠C=__________°.

Enter the value that correctly fills in the blank, like this: 42

Answer 1

In an isosceles triangle, the base angles are congruent. Therefore, m∠C = 3x + 5. The measure of all the angles in a triangle = 180°.

m∠A + m∠B + m∠C = 180

2x - 20 + 3x + 5 + 3x + 5 = 180°

8x - 10 = 180

8x = 190

x = 23.75°

m∠C = 3x + 5

m∠C = 3(23.75) + 5

m∠C = 71.25 + 5

m∠C = 76.25°

Answer 2

Following this video you must continue to solve for the value of X. Once, you obtain the value of X, remember that you are really looking for what is the measure of angle C. If you have further questions as to how to proceed with the problem, feel free to message :)