The fact that ∠E and ∠F are supplementary means that if you add their measures you will get 180°, which is the measure of a straight line.
m∠E + ∠F = 180
m∠E = 9x – 38
m∠F = 2x + 42
We can solve this system of equations by replacing the m∠E and the m∠F in the first equation. We then will have one equation with a single unknown, x.
m∠E + ∠F = 180
(9x – 38) + (2x + 42) = 180
9x – 38 + 2x + 42 = 180
Combine like terms to get:
11x + 4 = 180
Subtract 4 from each side to get:
11x = 176
Divide each side by 11 to find out what what a single x equals.
x = 16
Now you can answer half of your question: x is 16.
To figure out m∠F, go back to the equation that defines the value of m∠F and then replace the value of x, which is 16, for x in the equation:
m∠F = 2x + 42
m∠F = 2(16) + 42
m∠F = 32 + 42
m∠F = 74°
Now you know the question to the second question. The measure of ∠F is 74 degrees.
