Question

two angles are supplementary if their sum is 180°. the larger angle measures six degrees more than twice the measure of a smaller angle. if x represents the measure of the smaller angle and these two angles are supplementary, find the measure of each angle. the smaller angle measures °. the larger angle measures °.

Explanation:

Step1: Set up the equation

Let $x$ be the measure of the smaller angle. The larger angle measures six degrees more than twice the measure of the smaller angle, so the larger angle is $2x + 6$. Since the two angles are supplementary, their sum is $180^{\circ}$. So the equation is $x+(2x + 6)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $x+2x+6 = 3x+6$. So the equation becomes $3x+6 = 180$.

Step3: Solve for $x$

Subtract 6 from both sides: $3x=180 - 6=174$. Then divide both sides by 3: $x=\frac{174}{3}=58$.

Step4: Find the measure of the larger angle

Substitute $x = 58$ into the expression for the larger angle $2x+6$. So the larger angle is $2\times58+6=116 + 6=122$.

Answer:

The smaller angle measures $58^{\circ}$. The larger angle measures $122^{\circ}$.