Question

if there are 2 supplementary angles, angle 1 and 2, where angle 3 = (4x + 8) and angle 2 = (x + 17), and angle 4 is a vertical angle with angle 1, what is the measure of angle 4

Answer 1

To find the measure of angle 4, we first need to find the value of x. Since angle 3 and angle 2 are supplementary, their measures sum up to 180 degrees. So we have:

(4x + 8) + (x + 17) = 180
5x + 25 = 180
5x = 155
x = 31

Now that we have the value of x, we can find the measures of angle 3 and angle 2:
Angle 3 = 4(31) + 8 = 132 degrees
Angle 2 = 31 + 17 = 48 degrees

Since angle 1 and angle 4 are vertical angles, they have the same measure. Therefore, angle 4 = angle 1 = 132 degrees.