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?
A. 31
B. 132
C. 48
D. 124
Since ∠D and ∠E are supplementary angles, we have the equation ∠D + ∠E = 180°.
We can substitute the given expressions for ∠D and ∠E into the equation:
(4x+8) + (x+17) = 180
Combining like terms, we get:
5x + 25 = 180
Subtracting 25 from both sides, we have:
5x = 155
Dividing both sides by 5, we get:
x = 31
So ∠D = (4(31)+8) = 132° and ∠E = (31+17) = 48°.
Since ∠F is a vertical angle with ∠D, that means ∠F is also 132°.
Therefore, the measure of ∠F is 132°.
The answer is B.