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
31°
31 degrees
48°
48 degrees
132°
To find the measure of angle ∠F, we need to find the value of x.
Since ∠D and ∠E are supplementary angles, their measures add up to 180°. Therefore, we have the equation:
(4x + 8) + (x + 17) = 180
Simplifying the equation, we get:
5x + 25 = 180
Subtracting 25 from both sides:
5x = 155
Dividing both sides by 5:
x = 31
Now that we have the value of x, we can find the measure of angle ∠F.
∠F is a vertical angle with ∠D, so they have the same measure. Therefore, ∠F = ∠D = (4x + 8)° = (4(31) + 8)° = 124°.
Therefore, the measure of angle ∠F is 124°.