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
If ∠D and ∠E are supplementary angles, their sum is 180 degrees. Therefore, we have:
m<D + m<E = 180
(4x + 8) + (x + 17) = 180
5x + 25 = 180
Subtracting 25 from both sides:
5x = 155
Dividing by 5:
x = 31
Now, we can substitute this value of x back into the given equations to find the measures of ∠D and ∠E:
m<D = 4(31) + 8
= 124 + 8
= 132
m<E = 31 + 17
= 48
Since ∠F is a vertical angle with ∠D, they have equal measures. Therefore, m<F = 132 degrees.