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 132° 132 degrees 31° 31 degrees 48° 48 degrees 124°
Two angles are supplementary if their measures add up to 180 degrees.
Given that m∠D = (4x+8)° and m∠E = (x+17)°, we can set up the equation:
(4x+8)° + (x+17)° = 180°
Combining like terms, we get:
5x + 25 = 180
Subtracting 25 from both sides:
5x = 155
Dividing both sides by 5, we get:
x = 31
Now we can substitute the value of x back into the expression for ∠D to find its measure:
m∠D = (4(31)+8)° = 132°
Since ∠F is a vertical angle with ∠D, it has the same measure:
m∠F = 132°
Therefore, the measure of ∠F is 132 degrees. Answer: 132°