Question

the measure of an angle is eighty - nine times the measure of its supplementary angle. what is the measure of each angle? ° and °

Explanation:

Step1: Set up the equation

Let the measure of the supplementary angle be \(x\). Then the measure of the other angle is \(89x\). Since supplementary angles sum to \(180^{\circ}\), we have the equation \(x + 89x=180\).

Step2: Solve the equation

Combine like - terms: \(90x = 180\). Divide both sides by \(90\): \(x=\frac{180}{90}=2\).

Step3: Find the other angle

The other angle is \(89x\). Substitute \(x = 2\) into \(89x\), we get \(89\times2 = 178\).

Answer:

\(2\) and \(178\)