If there are two supplementary angles, ∠D

Question

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

132°
132 degrees

31°
31 degrees

48°

Answer 1

To find the measure of ∠F, we need to use the fact that ∠D and ∠E are supplementary angles, meaning they add up to 180 degrees.

So we can write the equation:

(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 we can find the measure of ∠F by substituting x = 31 into the expression for ∠D:

m∠F = (4x + 8) = (4 * 31 + 8) = 124 + 8 = 132

Therefore, the measure of ∠F is 132 degrees.