Question

find the measure of ∠fpy.

Explanation:

Step1: Recognize the relationship between angles

\(\angle FPY\) and the \(120^{\circ}\) angle are supplementary angles (they form a linear - pair).

Step2: Use the supplementary - angle formula

If two angles \(\alpha\) and \(\beta\) are supplementary, then \(\alpha+\beta = 180^{\circ}\). Let \(\alpha=\angle FPY\) and \(\beta = 120^{\circ}\). So, \(\angle FPY+120^{\circ}=180^{\circ}\).

Step3: Solve for \(\angle FPY\)

Subtract \(120^{\circ}\) from both sides of the equation: \(\angle FPY=180^{\circ}-120^{\circ}\).

$$ \angle FPY = 60^{\circ} $$

Answer:

\(60^{\circ}\)