Find Missing Angles Quick Check%0D%0A4 of 54 of 5 Items%0D%0A%0D%0AQuestion%0D%0AIf there are two supplementary angles, ∠D%0D%0A∠%0D%0A%0D%0A and ∠E%0D%0A∠%0D%0A%0D%0A, where m∠D=(4x+8)° and m∠E=(x+17)°, and ∠F is a vertical angle with ∠D, what is the measure of ∠F?%0D%0A%0D%0A %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A124°%0D%0A124 degrees%0D%0A%0D%0A48°%0D%0A48 degrees%0D%0A%0D%0A31°%0D%0A31 degrees%0D%0A%0D%0A132°

Answer 1

To find the measure of ∠F, we need to find the value of ∠D by using the given information.

Since ∠D and ∠E are supplementary angles, their measures add up to 180°:
∠D + ∠E = 180°

Substituting the given measures:
(4x + 8) + (x + 17) = 180

Simplifying the equation:
5x + 25 = 180
5x = 180 - 25
5x = 155
x = 31

Now that we have the value of x, we can find the measure of ∠D:
m∠D = (4x + 8)°
m∠D = (4(31) + 8)°
m∠D = (124 + 8)°
m∠D = 132°

Since ∠F is a vertical angle with ∠D, the measure of ∠F is also 132°.

Therefore, the measure of ∠F is 132°.