Question

find m∠knm. drag the expressions into the boxes to correctly complete the solution. m∠knm = 1/2(160 - 96) = 1/2( ) = 1/2( ) = 64° = 32° show hints

Explanation:

Step1: Find arc - length measures

The sum of the measures of the arcs of a circle is 360°. Given two arcs of measures 100° and 104°, the measure of the third arc is $360-(100 + 104)=156^{\circ}$. Let the two intercepted arcs of $\angle KNM$ be $a$ and $b$. Here, assume the larger arc $a = 160^{\circ}$ and the smaller arc $b=96^{\circ}$.

Step2: Apply the formula for the measure of an angle formed by two secants

The measure of an angle formed by two secants intersecting outside a circle is given by $m\angle\theta=\frac{1}{2}(a - b)$, where $a$ is the measure of the larger intercepted arc and $b$ is the measure of the smaller intercepted arc.
Substitute $a = 160^{\circ}$ and $b = 96^{\circ}$ into the formula: $m\angle KNM=\frac{1}{2}(160 - 96)$.
First, calculate $160-96 = 64^{\circ}$. Then, $\frac{1}{2}\times64^{\circ}=32^{\circ}$.

Answer:

$32^{\circ}$