Find Missing Angles Quick Check 4 of 54 of 5 Items Question 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 124° 124 degrees 48° 48 degrees 31°
To find the measure of ∠F, we need to find the value of x first.
Since ∠D and ∠E are supplementary, we can set up an equation:
m∠D + m∠E = 180°
(4x+8) + (x+17) = 180°
5x + 25 = 180°
5x = 155°
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)°
m∠D = (4(31)+8)°
m∠D = 132°
Since ∠F is a vertical angle with ∠D, ∠F will have the same measure as ∠D.
Therefore, the measure of ∠F is 132°.