Question

ray bf lies inside angle lbs. if angle lbs is a right - angle, and the measure of angle fbs is fourteen times the measure of angle lbf, find the measure of angle fbs. complete the statement. the measure of angle fbs is □°

Explanation:

Step1: Set up the relationship

Let the measure of angle $LBF$ be $x$. Then the measure of angle $FBS$ is $14x$. Since angle $LBS$ is a right - angle, and $\angle LBS=\angle LBF+\angle FBS$, we have $x + 14x=90^{\circ}$.

Step2: Solve the equation

Combining like terms, we get $15x = 90^{\circ}$. Then, dividing both sides by 15, we have $x=\frac{90^{\circ}}{15}=6^{\circ}$.

Step3: Find the measure of angle $FBS$

Since the measure of angle $FBS$ is $14x$, substituting $x = 6^{\circ}$, we get $\angle FBS=14\times6^{\circ}=84^{\circ}$.

Answer:

$84$