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
48°
48 degrees
132°
132 degrees
31°
To find the measure of angle ∠F, we need to use the fact that ∠D and ∠E are supplementary angles. This means that the sum of their measures is 180 degrees.
So, we can set up the equation:
(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 have the value of x, we can substitute it back into one of the angle measures to find the measure of ∠D:
m∠D = (4x + 8) = (4(31) + 8) = 124 degrees
Since ∠F is a vertical angle with ∠D, it has the same measure:
∠F = 124 degrees
The correct answer is 124°.