Question

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

Answer 1

Refer to the diagram shown below.

Because ΔABC is isosceles and AB = AC, therefore
m∠C = m∠B = (3x + 5)°

The sum of angles in a triangle is 180°, therefore
2(3x + 5) + 2x - 20 = 180
6x + 10 + 2x - 20 = 180
8x - 10 = 180
8x = 190
x = 23.75°

Therefore
m∠C = 3x + 5 = 3(23.75) + 5 = 76.25°

Answer: 76.25°