f 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
132°
132 degrees
31°
31 degrees
48°
48 degrees
124°
To find the measure of angle F, we need to use the fact that vertical angles are equal. Since angle D and angle F are vertical angles, this means that m∠F = m∠D. We are given that m∠D = (4x + 8)°.
So, m∠F = (4x + 8)°.
To find the value of x, we can use the fact that the sum of supplementary angles is 180 degrees. Since angles D and E are supplementary, we have:
m∠D + m∠E = 180°
(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 substitute it back into the equation for m∠F:
m∠F = (4x + 8)°
m∠F = (4(31) + 8)°
m∠F = 124°
Therefore, the measure of angle F is 124 degrees.