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?
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}
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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
F= 18
E= 72
Well, it seems that angle E and angle F are having a bit of a disagreement. Angle E is feeling 54 more important than angle F! I guess that means angle E is the drama queen of the two.
Let's play peacemaker and solve their little dispute. Since they are supplementary, their measures add up to 180 degrees. So we have:
Angle E + Angle F = 180
And we also know that Angle E is 54 more than Angle F, so we can write:
Angle E = Angle F + 54
Now, let's substitute the second equation into the first equation:
(Angle F + 54) + Angle F = 180
Combining like terms, we have:
2Angle F + 54 = 180
Subtracting 54 from both sides:
2Angle F = 126
Now, divide both sides by 2:
Angle F = 63
So, angle F is 63 degrees. Since angle E is 54 degrees more than angle F, we can add 54 to find:
Angle E = 63 + 54 = 117
So, angle E is 117 degrees. Angle F needs to realize that it's still a valuable angle, even if it's not as "extra" as angle E!
To find the measure of each angle, let's assign a variable to angle F.
Let's say angle F is represented by the variable 'x'.
Since angle E is 54 more than angle F, we can represent angle E as 'x + 54'.
Now, we know that angle E and angle F are supplementary, which means they add up to 180 degrees.
So, we can set up the equation:
angle E + angle F = 180
(x + 54) + x = 180
Simplifying the equation, we combine like terms:
2x + 54 = 180
Next, we'll isolate the variable by subtracting 54 from both sides:
2x = 180 - 54
2x = 126
Finally, we solve for x by dividing both sides by 2:
x = 126 / 2
x = 63
Therefore, angle F measures 63 degrees.
To find the measure of angle E, we substitute the value we found for x back into the equation:
angle E = x + 54
= 63 + 54
= 117
Therefore, angle E measures 117 degrees.
Thus, angle E measures 117 degrees and angle F measures 63 degrees.
x + x + 54 = 180
2x = 180 - 54
2x = 126
x = 63
63 + 54 = 117
http://www.mathsisfun.com/geometry/supplementary-angles.html