Question

use the image below to find the requested values.
find the measure of ∠bpk.
what is the value of y?

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles add up to \(180^{\circ}\). So, \(3y + 144=180\).

Step2: Solve the equation for \(y\)

Subtract \(144\) from both sides: \(3y=180 - 144\).
\(3y = 36\).
Divide both sides by \(3\): \(y=\frac{36}{3}=12\).

Step3: Find the measure of \(\angle BPK\)

Since \(\angle BPK=(3y)^{\circ}\) and \(y = 12\), then \(\angle BPK=3\times12 = 36^{\circ}\).

Answer:

The measure of \(\angle BPK\) is \(36^{\circ}\) and the value of \(y\) is \(12\).