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
132°
132 degrees
31°
31 degrees
48°
To find the measure of ∠F, we need to find the value of x first. Since ∠D and ∠E are supplementary angles, their measures should add up to 180°. Therefore, we can write the equation:
m∠D + m∠E = 180°
(4x + 8) + (x + 17) = 180
5x + 25 = 180
Subtract 25 from both sides:
5x = 155
Divide both sides by 5:
x = 31
Now that we know x = 31, we can substitute it back into the equations to find the measures of ∠D and ∠E:
m∠D = (4x + 8) = (4 * 31 + 8) = 124°
m∠E = (x + 17) = (31 + 17) = 48°
Since ∠F is a vertical angle with ∠D, it has the same measure as ∠D. So ∠F = m∠D = 124°.
Therefore, the measure of ∠F is 124 degrees.