Question

use the equations and the diagram of the circle to answer the quest below. m\widehat{ bhf }=150° y = 54° what is the measure of \widehat{ cgj }? 75° 31° 42° 108°

Explanation:

Step1: Recall the formula for the measure of an angle formed by two secants outside the circle

The measure of an angle formed by two secants outside the circle is \(y=\frac{1}{2}(m\overparen{BHF}-m\overparen{CGJ})\).

Step2: Substitute the given values into the formula

We know that \(y = 54^{\circ}\) and \(m\overparen{BHF}=150^{\circ}\). Substituting these values into the formula \(54^{\circ}=\frac{1}{2}(150^{\circ}-m\overparen{CGJ})\).

Step3: Solve the equation for \(m\overparen{CGJ}\)

First, multiply both sides of the equation by \(2\): \(2\times54^{\circ}=150^{\circ}-m\overparen{CGJ}\), so \(108^{\circ}=150^{\circ}-m\overparen{CGJ}\). Then, we can rewrite it as \(m\overparen{CGJ}=150^{\circ}- 108^{\circ}\).

Answer:

\(42^{\circ}\)