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) Responses 124° 124 degrees 48° 48 degrees 31° 31 degrees 132°
We know that supplementary angles add up to 180 degrees. Therefore, we can write the equation: ∠D + ∠E = 180.
Substituting the given values, we get:
(4x + 8) + (x + 17) = 180
Combining like terms, we have:
5x + 25 = 180
Subtracting 25 from both sides, we get:
5x = 155
Dividing both sides by 5, we have:
x = 31
Now, we can find the measure of ∠D:
m∠D = (4x + 8) = (4 * 31 + 8) = 124 degrees
Since ∠F is a vertical angle with ∠D, ∠F must also measure 124 degrees.
The answer is 124°.