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 ? (1 point)
48°
132°
31°
124°
To solve this problem, we need to use the fact that vertical angles are equal in measure.
Since ∠F is a vertical angle with ∠D, we know that the measure of ∠F is the same as ∠D, which is (4x+8)°.
We can now set up an equation to find the value of x:
∠D + ∠E = 180° (since the angles are supplementary)
(4x+8)° + (x+17)° = 180°
Combining like terms, we get:
5x + 25 = 180
Now, let's solve for x:
5x = 155
x = 31
Therefore, the measure of ∠F is (4x+8)° = (4*31+8)° = 132°.
The measure of ∠F is 132°, so the correct answer is B.