Question

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

Explanation:

Step1: Set up variables

Let the measure of the supplementary angle be \(x\) degrees. Then the measure of the other angle is \(39x\) degrees.

Step2: Use the supplementary - angle relationship

Since two supplementary angles add up to \(180^{\circ}\), we have the equation \(x + 39x=180\).
Simplify the left - hand side: \(40x = 180\).

Step3: Solve for \(x\)

Divide both sides of the equation \(40x = 180\) by \(40\): \(x=\frac{180}{40}=4.5\).

Step4: Find the measure of the other angle

The other angle is \(39x\). Substitute \(x = 4.5\) into \(39x\), we get \(39\times4.5 = 175.5\).

Answer:

\(4.5\) and \(175.5\)