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°
48°
Explanation: Since ∠D and ∠E are supplementary, the sum of their measures is 180°. So, (4x+8) + (x+17) = 180. Solving for x, we get x = 27.
Since ∠F is a vertical angle with ∠D, the measure of ∠F is also 4x+8. Substituting x = 27, we get the measure of ∠F = 4(27) + 8 = 108 + 8 = 116°.
Therefore, the measure of ∠F is 116°.
no
Apologies for the error in my previous response. Let's try solving this again.
Since ∠D and ∠E are supplementary angles, we have:
m∠D + m∠E = 180°
Substitute the given measures of ∠D and ∠E:
(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 found x, we can determine the measures of ∠D and ∠E:
m∠D = 4(31) + 8 = 124°
m∠E = 31 + 17 = 48°
Since ∠F is a vertical angle with ∠D, the measure of ∠F is the same as ∠D:
∠F = 124°
Therefore, the measure of ∠F is 124°.