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Chapter 2: Problem 50

Use the five-step problem-solving strategy to find the measure of the angle described. The measure of the angle's supplement is \(52^{\circ}\) more than twice that of its complement.

Short Answer

Expert verified
The measure of the angle is \(52^{\circ}\).

Step by step solution

01

Setting up the equation

Let's denote the angle we are looking for by x. According to the problem, the supplement of the angle (which is \(180^{\circ} - x\)) is 52 degrees more than twice its complement (which is \(90^{\circ} - x\)). We can express this as an equation: \(180^{\circ} - x = 2 * (90^{\circ} - x) + 52^{\circ}\).
02

Simplifying the equation

When we expand the right side of the equation, we end up with: \(180^{\circ} - x = 180^{\circ} - 2x + 52^{\circ}\). We can then simplify the equation by canceling out the \(180^{\circ}\) on both sides: \(-x = -2x + 52^{\circ}\).
03

Solving the equation

Adding 2x to both sides of the equation gives: \(x = 52^{\circ}\). Hence, the measure of the angle is \(52^{\circ}\).
04

Verify the solution

We can validate the answer by checking if the supplement of the angle (\(180^{\circ} - 52^{\circ} = 128^{\circ}\)) is indeed 52 degrees more than twice its complement (which is \(90^{\circ} - 52^{\circ} = 38^{\circ}\), and twice this is \(76^{\circ}\). Adding 52 to 76 gives us 128 degrees, thus confirming our solution is correct.

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