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
Since <D and <E are supplementary angles, their measures sum up to 180 degrees. Therefore, we have the equation:
m<D + m<E = 180
(4x+8) + (-(x+17)) = 180
Simplifying the equation:
4x + 8 - x - 17 = 180
3x - 9 = 180
Add 9 to each side:
3x = 189
Divide each side by 3:
x = 63
Now, we can find the measure of <D:
m<D = 4x + 8 = 4(63) + 8 = 252 + 8 = 260
Since F is a vertical angle with D, their measures are congruent. Therefore, the measure of F is also 260 degrees.