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

1 Answer
Dec 27, 2016

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^@#