Question

question 5 (multiple choice worth 2 points) (angle relationships mc) angles x and y are supplementary. angle x measures 115.75° and angle y measures (m - 8)°. find m∠y. 136.5° 128.5° 72.25° 64.25°

Explanation:

Step1: Use the supplementary angles property

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle X + m\angle Y=180^{\circ}\).
Given \(m\angle X = 115.75^{\circ}\) and \(m\angle Y=(m - 8)^{\circ}\), we have \(115.75+(m - 8)=180\).

Step2: Solve for \(m\angle Y\)

First, simplify the left - hand side of the equation: \(115.75+m - 8=m + 107.75\).
Then, solve \(m + 107.75=180\) for \(m\). Subtract \(107.75\) from both sides: \(m=180 - 107.75=72.25\).
Now, find \(m\angle Y\). Since \(m\angle Y=(m - 8)^{\circ}\), substitute \(m = 72.25\) into the formula. \(m\angle Y=(72.25-8)^{\circ}=64.25^{\circ}\).

Answer:

\(64.25^{\circ}\)