Question

ΔABC is an isosceles triangle in which angles B and C are congruent. If m∠B = (2x + 16)° and m∠C = (3x - 11)°, find the measure of angle A.

A) 27°
B) 40°
C) 60°
D) 70°

Answer 1

40 is the answer. You have to find x by making the two equations equal the same then solve for x. Then plug in x to both equations to get the sum, add them together, then subtract it from 180 to get the sum of the last angle

Answer 2

2x + 16 = 3x - 11 because angles B and C are congruent
3x -2x = 16 + 11
x = 27

m<B = 2x + 16
m<B = 2(27) + 16
m<B = 56+16
m<B = 70

because B and C are congruent
m<B = m<C = 70
so 

m<A = 180 - ( 70+70)
m<A = 180 - 140
m<A = 180 = 40

answer is B) 40°