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
124°
124 degrees
132°
132 degrees
31°
31 degrees
48°
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.