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
31°
31 degrees
132°
132 degrees
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page 12 of 12
To find the measure of angle F, we need to determine the value of x. Since angles D and E are supplementary, we have the equation:
m∠D + m∠E = 180°
Substituting the given measures, we get:
(4x + 8)° + (x + 17)° = 180°
Simplifying, we combine 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 find the measure of angle D:
m∠D = (4x + 8)° = (4(31) + 8)° = 132°
Since angle F is a vertical angle to angle D, it has the same measure:
m∠F = 132°
Therefore, the measure of angle F is 132 degrees.