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