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 ?
Responses:
132°
31°
48°
124°
To find the measure of ∠F, we need to know the measure of ∠D. Given that m∠D = (4x+8)°, we can set up an equation:
m∠D + m∠E = 180°
(4x+8)° + (x+17)° = 180°
Combine like terms:
5x + 25 = 180
Subtract 25 from both sides:
5x = 155
Divide both sides by 5:
x = 31
Now that we know the value of x, we can find the measure of ∠D:
m∠D = (4x+8)°
m∠D = (4(31)+8)°
m∠D = 124°
Since ∠F is a vertical angle with ∠D, ∠F will have the same measure as ∠D.
Therefore, the measure of ∠F is 124°.