Question

`triangleABC` is isosceles, where AB=BC. If `m angleA= 5x+ 30` and `mangleB= 2x`, then how do you find `mangleC`?

Answer 1

Please see the explanation.

Explanation:

Given: `angle A = 5x + 30^@, angle B = 2x, and AB = BC`

I am going to use the notation where the side opposite the angle has the same letter but in lowercase. In this notation, AB becomes side c and BC becomes side a, therefore, AB = BC becomes c = a

Because c = a, we know that `angle A = angle C = 5x + 30^@`; this allows us to write the following equation:

`angle A + angle B + angle C = 180^@`

Substitute the corresponding functions of x:

`5x + 30 + 2x + 5x + 30 = 180^@`

Solve for x:

`12x + 60^2 = 180^@`

`12x = 120^@`

`x = 10^@`

`angle C = 5(10^@) + 30^@`

`angle C = 80^@`