In the figure below, lines r and s are parallel. what is the measure of angle three? explain how you know.

We need to solve first the value of x from the given figure. Angle 3 and the angle = 10x have the same measurements because they are pair VERTICAL ANGLES. The angle = 10x and the angle = 4x + 42 have equal angle measures as well because they are pair CORRESPONDING ANGLES. Therefore in solving angle 3, we start by solving angle = 10x and angle = 4x + 42. That is by equating the two given angles. We have 10x = 4x +42. Solving for x, we get x = 7. To solve for ANGLE 3. we simply substitute x = 7 to angle = 10x which also equal to angle 3. Therefore, ANGLE 3 measures, 70 degrees. (10*7)

Angle 3 is vertical to the angle with 10x.
The angle with 10x is equal to the angle with 4x + 42.
Set up an equation:
10x = 4x + 42
subtract 4x from both sides
6x = 42
x = 7
10(7) = 70
Angle 3 = 70 degrees