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