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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.

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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.

This problem has been solved

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