Question

1. geometry supplementary angles are two angles with measures that have a sum of 180°. complementary angles are two angles with measures that have a sum of 90°. the measure of the supplement of an angle is 10° more than twice the measure of the complement of the angle. let 90 - x equal the degree measure of the complement angle and 180 - x equal the degree measure of the supplement angle. write and solve an equation to find the measure of the angle.

Explanation:

Step1: Set up the equation

We are given that the measure of the supplement of an angle is 10° more than twice the measure of the complement of the angle. If the complement of the angle is \(90 - x\) and the supplement is \(180 - x\), the equation is \(180 - x=2(90 - x)+ 10\).

Step2: Expand the right - hand side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(2(90 - x)\) to get \(180-2x\). So the equation becomes \(180 - x=180-2x + 10\).

Step3: Simplify the equation

Subtract 180 from both sides of the equation: \((180 - x)-180=(180-2x + 10)-180\), which simplifies to \(-x=-2x + 10\).

Step4: Solve for \(x\)

Add \(2x\) to both sides of the equation: \(-x+2x=-2x + 10+2x\). This gives \(x = 10\).

Answer:

The measure of the angle is \(10^{\circ}\)