Question

an angle measures 56° less than the measure of its supplementary angle. what is the measure of each angle?

Explanation:

Step1: Let the measure of the supplementary angle be \( x \) degrees.

Let the measure of the given angle be \( y \) degrees. We know that \( y=x - 56\) and \(x + y=180\) (since supplementary angles sum to \(180^{\circ}\)).

Step2: Substitute \( y=x - 56\) into \(x + y=180\).

We get \(x+(x - 56)=180\). Simplify the left - hand side: \(2x-56 = 180\).

Step3: Solve for \(x\).

Add \(56\) to both sides: \(2x=180 + 56=236\). Then divide both sides by \(2\): \(x=\frac{236}{2}=118\).

Step4: Solve for \(y\).

Since \(y=x - 56\), substitute \(x = 118\) into the equation: \(y=118-56 = 62\).

Answer:

\(62\) and \(118\)