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

48°
48 degrees

124°
124 degrees

132°
132 degrees

31°
31 degrees
Skip to navigation
page 12 of 12

Answer 1

To find the measure of ∠F, we need to find the value of x. Since ∠D and ∠E are supplementary angles, their measures add up to 180 degrees.

Therefore: (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 that we know the value of x, we can find the measure of ∠F by substituting it into the measure of ∠D:

∠F = ∠D = (4x+8) = (4*31 + 8) = 124 degrees

Therefore, the measure of ∠F is 124 degrees.