Question

Angle E and angle F are supplementary. The measure of angle E is 54 more than the measure of angle F. What is the measure of each angle?

Answer 1

x + x + 54 = 180

2x = 180 - 54

2x = 126

x = 63

63 + 54 = 117

http://www.mathsisfun.com/geometry/supplementary-angles.html

Answer 2

here is the same reasoning but better explained
make both angles the same variable
X+X+54=180 {then group both of the X together}
2X+54 = 180
-54 = -54 {subtract 54 from both sides}
----------------------------------------------------------
2X = 126
divide 2 from both sides to get x alone
X=63 so angle f is 63

now we find angle e

take the 63 that represents f and put it in the new equation :)
and add the 54 from the 1st equation to get angle e
63+54=117
177 is angle e

so your answer all together is angle E=117 and angle F=63

Answer 3

F= 18
E= 72