Answer:
x = 15; y = 21
Step-by-step explanation:
The vertical angles have the same measure.
The sum of the measures of the angles of a triangle is 180 deg.
Left triangle:
4y - 18 + y + 14 + 6x - 11 = 180 Equation 1
Right triangle:
6x - 11 + 81 + x + 5 = 180 Equation 2
Simplify Equation 1.
4y - 18 + y + 14 + 6x - 11 = 180
6x + 5y = 195 Equation 3
Simplify Equation 2.
6x - 11 + 81 + x + 5 = 180
7x = 105
Solve last equation for x.
7x/7 = 105/7
x = 15
Substitute 15 for x in Equation 3 and solve for y.
6x + 5y = 195
6(15) + 5y = 195
90 + 5y = 195
5y = 105
y = 21
Answer: x = 15; y = 21
