Question

if ( \text{m}overarc{cm} = 36^circ ) and ( \text{m}angle t = 35^circ ), find ( \text{m}overarc{lk} ).

( \text{m}overarc{lk} = )

Explanation:

Step1: Recall the formula for an angle formed by two secants outside a circle.

The measure of an angle formed by two secants intersecting outside a circle is half the difference of the measures of the intercepted arcs. The formula is \( m\angle T=\frac{1}{2}(m\widehat{LK} - m\widehat{CM}) \).

Step2: Substitute the known values into the formula.

We know that \( m\angle T = 35^{\circ} \) and \( m\widehat{CM}=36^{\circ} \). Substituting these into the formula \( 35^{\circ}=\frac{1}{2}(m\widehat{LK}- 36^{\circ}) \).

Step3: Solve for \( m\widehat{LK} \).

First, multiply both sides of the equation by 2: \( 2\times35^{\circ}=m\widehat{LK}- 36^{\circ} \), which simplifies to \( 70^{\circ}=m\widehat{LK}- 36^{\circ} \). Then, add \( 36^{\circ} \) to both sides: \( m\widehat{LK}=70^{\circ}+ 36^{\circ}=106^{\circ} \).

Answer:

\( 106^{\circ} \)