Question

an angle measures 51.4° less than the measure of its supplementary angle. what is the measure of each angle? submit

Explanation:

Step1: Set up equations

Let the measure of the angle be \(x\) and its supplement be \(y\). We know that \(x + y=180\) (supplementary angles) and \(x=y - 51.4\).

Step2: Substitute and solve

Substitute \(x=y - 51.4\) into \(x + y=180\).
\((y - 51.4)+y=180\)
\(2y-51.4 = 180\)
\(2y=180 + 51.4\)
\(2y=231.4\)
\(y=\frac{231.4}{2}=115.7\)
Then \(x=y - 51.4=115.7-51.4 = 64.3\)

Answer:

\(64.3\) and \(115.7\)