Question

Use an algebraic approach to solve the problem.

If the complement of an angle is 5° less than one-sixth of its supplement, find the measure of the angle.
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Answer 1

To solve the problem, we need to find the measure of an angle using an algebraic approach. The measure of the angle can be obtained by setting up an equation based on the given information and then solving it. In this case, the measure of the angle is 120 degrees.

Step-by-step explanation:

Let's assume the angle we need to find is x degrees.

According to the problem, the complement of the angle is 5° less than one-sixth of its supplement. The complement of x degrees is 90 - x degrees, and the supplement of x degrees is 180 - x degrees. Therefore, we can set up the equation:

(90 - x) = 5 + (1/6)(180 - x)

Now, let's solve the equation:

90 - x = 5 + (30 - x)/ 6

90 - x = 5 + (30 - x)/ 6

540 - 6x = 30 - x + 30 - x

540 - 6x = 60 - 2x

540 = 60 + 4x

480 = 4x

x = 120

The measure of the angle is 120 degrees.

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