Question

use the image below to find the requested values. find the measure of \\( \angle bcp \\).

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles add up to \(180^{\circ}\). Let \(\angle BCP = 6m\) and the adjacent angle be \(150^{\circ}\). Then \(6m+150 = 180\).

Step2: Solve the equation for \(m\)

Subtract \(150\) from both sides of the equation \(6m+150 = 180\). We get \(6m=180 - 150\), so \(6m = 30\). Then divide both sides by \(6\), \(m=\frac{30}{6}=5\). But the question asks for \(\angle BCP\). Since \(\angle BCP\) and the \(150^{\circ}\) angle are supplementary (they form a linear - pair), \(\angle BCP=180 - 150\).

Answer:

\(30^{\circ}\)