Question

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

Explanation:

Step1: Recall angle - subtraction formula for angles formed by two secants

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 sum of the measures of the arcs of a circle is 360°. So the third arc measure is \(360-(160 + 104)=96^{\circ}\).

Step2: First blank

The formula for \(m\angle KNM=\frac{1}{2}(\text{major arc}-\text{minor arc})\), so the first blank is \((\text{measure of arc }KML-\text{measure of arc }KL)\).

Step3: Second blank

Since arc \(KML = 160^{\circ}\) and we found the other - arc (the one not 160° and 104°) is 96°, the second blank is \((160 - 96)\).

Step4: Third blank

\(\frac{1}{2}(160 - 96)=\frac{1}{2}(64)\).

Step5: Fourth blank

\(\frac{1}{2}(64)=32\).

Answer:

First blank: Measure of arc \(KML-\text{measure of arc }KL\)
Second blank: \(160 - 96\)
Third blank: \(64\)
Fourth blank: \(32\)