Answer:
x = 4
z = 84
Step-by-step explanation:
The angles with measures (5x+ 76) and (15x + 36) are vertical because they are opposite and formed by the intersection of two lines.
Vertical angles have the same measure, so, we can write the following equation:
5x + 76 = 15x + 36
Solving for x, we get:
5x + 76 - 36 = 15x + 36 - 36
5x + 40 = 15x
5x + 40 - 5x = 15x - 5x
40 = 10x
40/10 = 10x/10
4 = x
So, the value of x is 4.
Then, angle with measure z and angle (15x + 36) form a straight line. So, their sum is 180 and we can write the following equation:
z + (15x + 36) = 180
Replacing the value of x = 4 and solving for z, we get:
z + 15(4) + 36 = 180
z + 60 + 36 = 180
z + 96 = 180
z + 96 - 96 = 180 - 96
z = 84
Therefore, the answers are:
x = 4
z = 84