Answer:
x = 11
z = 86
Explanation:
8x + 6 and 10x-16 are vertical angles
Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.
To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:
8x + 6 - 6 = 10x - 16 - 6
8x = 10x - 22
Now we can subtract 8x from both sides of the equation:
8x - 8x = 10x - 22 - 8x
0 = 2x - 22
To solve for x, we can add 22 to both sides of the equation:
0 + 22 = 2x - 22 + 22
22 = 2x
Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2
x = 11
Therefore, the solution to the equation is x = 11.
Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)
Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.
First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94
180 - 94 = z
z = 86