Question

angles x and y are supplementary. angle x measures 132.54°, and angle y measures (m - 15)°. find m∠y.
47.46°
62.46°
85.08°
117.54°

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle X + m\angle Y=180^{\circ}\).
Given \(m\angle X = 132.54^{\circ}\) and \(m\angle Y=(m - 15)^{\circ}\), we substitute into the equation: \(132.54+(m - 15)=180\).

Step2: Solve the equation for \(m\)

First, simplify the left - hand side of the equation: \(132.54+m-15 = 180\).
\(m+117.54 = 180\).
Then, subtract \(117.54\) from both sides: \(m=180 - 117.54\).
\(m = 62.46\).

Step3: Find \(m\angle Y\)

Since \(m\angle Y=(m - 15)^{\circ}\), substitute \(m = 62.46\) into the formula.
\(m\angle Y=(62.46-15)^{\circ}\).
\(m\angle Y = 47.46^{\circ}\).

Answer:

\(47.46^{\circ}\)