If there are two supplementary angles where ∠D=4x+8° and ∠E=x+17°, and ∠F is a vertical angle with ∠D, what is the measure of ∠F?
Supplementary angles add up to 180 degrees, so:
∠D + ∠E = 180
Substituting in the given values:
4x + 8 + x + 17 = 180
Simplifying and solving for x:
5x + 25 = 180
5x = 155
x = 31
So ∠E = 31 + 17 = 48 degrees.
∠F is a vertical angle with ∠D, so it is also equal to 4x + 8 degrees. Substituting in x = 31:
∠F = 4(31) + 8 = 132 degrees.