Question

1. connecting concepts angle ( x ) and angle ( y ) are complementary angles. the measure of angle ( y ) is 6 less than twice the measure of angle ( x ). what is the measure of each angle?

Explanation:

Step1: Set up equations

Let the measure of angle \(X\) be \(x\) degrees. Since angle \(X\) and angle \(Y\) are complementary, \(x + y=90\). Also, given that \(y = 2x-6\).

Step2: Substitute \(y\) in the first equation

Substitute \(y = 2x - 6\) into \(x + y=90\). We get \(x+(2x - 6)=90\).
Simplify the left - hand side: \(x+2x-6 = 3x-6\). So, \(3x-6 = 90\).

Step3: Solve for \(x\)

Add \(6\) to both sides of the equation \(3x-6 = 90\): \(3x-6 + 6=90 + 6\), which gives \(3x=96\).
Divide both sides by \(3\): \(x=\frac{96}{3}=32\).

Step4: Solve for \(y\)

Substitute \(x = 32\) into \(y = 2x-6\). Then \(y=2\times32-6\).
First, calculate \(2\times32 = 64\). Then \(y=64 - 6=58\).

Answer:

The measure of angle \(X\) is \(32^{\circ}\) and the measure of angle \(Y\) is \(58^{\circ}\).