Question

find m\\(\overparen{km}\\). drag the correct answers into the boxes. hide hints recall that m\\(\angle knm=\frac{1}{2}(m\\(\overparen{km}-m\\(\overparen{lk})\\) m\\(\angle knm =\frac{1}{2}(m\\(\overparen{km}-m\\(\overparen{lk})\\)

Explanation:

Step1: Recall the secant - secant angle formula

The measure of an angle formed by two secants intersecting outside a circle is given by $m\angle KNM=\frac{1}{2}(m\overparen{KM}-m\overparen{LK})$. We know that $m\angle KNM = 22^{\circ}$. Let $m\overparen{KM}=x$ and assume $m\overparen{LK} = 95^{\circ}$ (from the figure).
So, $22^{\circ}=\frac{1}{2}(x - 95^{\circ})$.

Step2: Solve the equation for $x$

Multiply both sides of the equation $22^{\circ}=\frac{1}{2}(x - 95^{\circ})$ by 2:
$2\times22^{\circ}=x - 95^{\circ}$.
$44^{\circ}=x - 95^{\circ}$.
Then add $95^{\circ}$ to both sides:
$x=m\overparen{KM}=44^{\circ}+ 95^{\circ}=139^{\circ}$.

Answer:

$139^{\circ}$