If there are two supplementary angles, D and E, where m D=(4x+8) and m E=(x+17), and F is a vertical angle with D, what is the measure of F?

Answer 1

Since D and E are supplementary angles, we know that their measures must add up to 180 degrees. So, we can set up the following equation:

(4x + 8) + (x + 17) = 180

Combine like terms:

5x + 25 = 180

Subtract 25 from both sides:

5x = 155

Divide by 5:

x = 31

Now, we can plug x back into the equation for the measure of angle E:

m E = x + 17
m E = 31 + 17
m E = 48

Therefore, the measure of angle E is 48 degrees.

Since vertical angles are congruent, the measure of angle F is also 48 degrees.