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 ?
Since ∠D and ∠E are supplementary angles, their measures add up to 180 degrees.
m∠D + m∠E = 180
(4x + 8) + (x + 17) = 180
5x + 25 = 180
5x = 155
x = 31
Therefore, m∠D = 4(31) + 8 = 132 degrees.
Since ∠F is a vertical angle with ∠D, they have the same measure.
Therefore, m∠F = m∠D = 132 degrees.