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
31°
31 degrees
132°
132 degrees
48°
48 degrees
124°
To find the measure of angle ∠F, we need to find the value of x. Since angle ∠D and ∠E are supplementary angles, their measures add up to 180 degrees. So we can set up the equation:
m∠D + m∠E = 180
(4x+8) + (x+17) = 180
Combine like terms:
5x + 25 = 180
Subtract 25 from both sides:
5x = 155
Divide both sides by 5:
x = 31
Now that we know the value of x, we can find the measure of angle ∠F, which is equal to ∠D.
m∠F = m∠D = (4x+8) = (4(31)+8) = 124 degrees.
Therefore, the measure of ∠F is 124°.