Question

pool felipe uses a computer program to model the paths of pool balls. \\( \angle g f h \\) is a straight angle that represents the rail of the pool table. if \\( \overrightarrow{f k} \\) bisects \\( \angle j f l \\), and \\( m \angle j f l=90^{\circ} \\), what is \\( m \angle j f k \\)?

Explanation:

Step1: Recall the angle - bisector definition

An angle bisector divides an angle into two equal parts. If \( \overrightarrow{FK}\) bisects \( \angle JFL\), then \( \angle JFK=\angle KFL\).

Step2: Use the formula for the measure of angles formed by an angle bisector

Let \( m\angle JFK = x\) and \( m\angle KFL=x\) (since \( \overrightarrow{FK}\) bisects \( \angle JFL\)). We know that \( m\angle JFL=m\angle JFK + m\angle KFL\). Given \( m\angle JFL = 90^{\circ}\).
Substitute into the equation: \(90^{\circ}=x + x\).

Step3: Solve the equation for \(x\)

Combine like terms: \(90^{\circ}=2x\).
Divide both sides by 2: \(x=\frac{90^{\circ}}{2}=45^{\circ}\).

Answer:

\(45^{\circ}\)