Two angles are supplementary. The larger angle is 66 degrees larger then the smaller angle. Find the measure of both angles?

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The answer is #57° and 123°#.

Explanation:

A supplementary angle is an angle that equals #180°#. So now we know that the two angles added together will give us #180°#, we can use this to check at the end.

Let's call the smaller angle #x#
We also know that the larger number is #66°# more than the smaller. This gives us:

# x + x + 66° = 180°#.

x is equal to the smaller angle, and the second angle is #( x)# - the smaller number with an extra #66°#, giving us the difference.

Now we can simplify this by subtracting #66°# from both sides.

#x+x+66°-66° = 180°-66°#

(balancing the equation) and get

#x + x = 114. #

#2x = 114#

Next, we can divide #114# by #2# as there are #2x's#,

#(2x)/2 = 114/2#

giving us # x=57#.

#57# is, therefore, the smaller angle.

To get the larger angle we can either subtract: #180°-57 = 123°#

or add: #66° + 5° = 123°#

Both answers give us #123.#

To check our answer, we can add:

# 57° + 123° =180°#, and proving the answer.

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