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

Answer 1

Since <D and <E are supplementary angles, the sum of their measures is 180 degrees. We can represent this as an equation:

m<D + m<E = 180

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

Combining like terms:

5x + 25 = 180

Subtracting 25 from both sides:

5x = 155

Dividing both sides by 5:

x = 31

To find the measure of <F, we need to know the measure of <D. Substituting x = 31 into the equation for <D:

m<D = 4(31) + 8 = 124 + 8 = 132 degrees

Since <F is a vertical angle with <D, they have equal measures. Therefore, the measure of <F is also 132 degrees.