Questions: Use an algebraic approach to find the measure of the two angles described below. Begin by letting x represent the degree measure of the angle complement. What is the measure of the complement? What is the measure of the angle? The measure of the angle is 76 degrees greater than its complement.

Solution Steps

To solve this problem, we need to set up an equation based on the relationship between the angle and its complement. Let \( x \) be the measure of the complement. The angle is then \( x + 76 \) degrees. Since the sum of an angle and its complement is 90 degrees, we can set up the equation \( x + (x + 76) = 90 \). Solving this equation will give us the measure of the complement, and subsequently, the measure of the angle.

Let \( x \) be the measure of the complement of the angle. The angle can then be expressed as \( x + 76 \). Since the sum of an angle and its complement is \( 90 \) degrees, we can set up the equation: \[ x + (x + 76) = 90 \]

Simplifying the equation gives: \[ 2x + 76 = 90 \]

To isolate \( x \), we subtract \( 76 \) from both sides: \[ 2x = 90 - 76 \] \[ 2x = 14 \] Dividing both sides by \( 2 \) yields: \[ x = 7 \]

Now that we have the measure of the complement, we can find the measure of the angle: \[ \text{Angle} = x + 76 = 7 + 76 = 83 \]

Final Answer