The difference in the measures of two supplementary angles is 26°. Find the measure of the angles.
Question
The difference in the measures of two supplementary angles is 26°. Find the measure of the angles.
Solution
Let's assume that one angle measures x degrees. Since the angles are supplementary, the other angle would measure (180 - x) degrees.
According to the given information, the difference between the measures of the two angles is 26 degrees. So, we can set up the equation:
(180 - x) - x = 26
Simplifying the equation, we have:
180 - 2x = 26
Now, let's solve for x:
180 - 26 = 2x
154 = 2x
Dividing both sides by 2, we get:
x = 77
Therefore, one angle measures 77 degrees, and the other angle measures (180 - 77) = 103 degrees.
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