Question

if ( moverparen{gv}=42^{circ}) and ( mangle a = 44^{circ}), find ( moverparen{li})

Explanation:

Step1: Use the formula for the measure of an angle formed by two secants

The formula is \(m\angle A=\frac{1}{2}(m\overparen{LI}-m\overparen{GU})\).

Step2: Substitute the known values into the formula

Given \(m\angle A = 44^{\circ}\) and \(m\overparen{GU}=42^{\circ}\), we have \(44^{\circ}=\frac{1}{2}(m\overparen{LI}- 42^{\circ})\).

Step3: Solve for \(m\overparen{LI}\)

Multiply both sides by \(2\): \(44^{\circ}\times2=m\overparen{LI}-42^{\circ}\), so \(88^{\circ}=m\overparen{LI}-42^{\circ}\).
Then add \(42^{\circ}\) to both sides: \(m\overparen{LI}=88^{\circ}+ 42^{\circ}\).

Answer:

\(m\overparen{LI}=130^{\circ}\)