f 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) Responses 132° 132 degrees 48° 48 degrees 124° 124 degrees 31° 31 degrees
The measure of ∠D is (4x+8)° and the measure of ∠E is (x+17)°. Since ∠D and ∠E are supplementary angles, we know that their sum is 180°.
(4x+8)° + (x+17)° = 180°
Combining like terms, we get:
5x + 25 = 180
Subtracting 25 from both sides:
5x = 155
Dividing both sides by 5:
x = 31
Now that we know x is 31, we can find the measure of ∠D:
∠D = 4x + 8 = 4(31) + 8 = 124°
Since ∠F is a vertical angle with ∠D, ∠F must have the same measure as ∠D. Therefore, the measure of ∠F is 124°.
So, the correct answer is 124°.