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
132°
132 degrees
31°
31 degrees
124°
124 degrees
48°
To find the measure of ∠F, we need to find the value of x first.
Since ∠D and ∠E are supplementary angles, we can set up the equation:
(4x+8) + (x+17) = 180
Combining like terms, we get:
5x + 25 = 180
Subtracting 25 from both sides, we have:
5x = 155
Dividing both sides by 5, we get:
x = 31
Now that we have the value of x, we can substitute it back into the equation for ∠D to find its measure:
m∠D = (4x+8)° = (4(31)+8)° = 132°
Since ∠F is a vertical angle with ∠D, their measures will be equal. Therefore, the measure of ∠F is 132°.
So the correct answer is: 132°.