Answer:
A = 114°, B = C = 33°
Step-by-step explanation:
The triangle relationships let you write two equations:
A+B+C = 180
B=C
Substituting the expressions for A, B, and C, you have ...
(x+7y+41) +(2y+13) +(6x+15) = 180
7x +9y +69 = 180
7x +9y = 111
And the second equation gives ...
(2y+13) = (6x+15)
6x -2y =-2
3x -y = -1
Now, we can add 9 times this second equation to the first to eliminate the y-variable.
(7x +9y) +9(3x -y) = (111) +9(-1)
34x = 102
x = 3
Then the angle measures are ..
B = C = 6·3+15 = 33
A = 180 -2·33 = 114
The angles in the triangle are (A, B, C) = (114°, 33°, 33°).
