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) 124°
B) 31°
C) 132°
D) 48°
The sum of two supplementary angles is 180 degrees.
Therefore, we can set up the equation:
(4x + 8) + (x + 17) = 180
Combining like terms:
5x + 25 = 180
Subtracting 25 from both sides:
5x = 155
Dividing both sides by 5:
x = 31
Now we can find the measure of ∠F, which is a vertical angle with ∠D.
∠F will have the same measure as ∠D.
Plugging x = 31 into the equation for ∠D:
m∠D = (4x + 8)° = (4(31) + 8)° = 132°
Therefore, the measure of ∠F is 132°.
The answer is C) 132°.