Question

in the diagram, m∠lmn = 116, m∠jkm = 122, and m∠jnm = 103. what is m∠nkm? m∠nkm = (simplify your answer. do not include the degree symbol in your answer.)

Explanation:

Step1: Recall the sum of angles in a quadrilateral

The sum of the interior angles of a quadrilateral is 360°. In quadrilateral JNML, we know three - angles: \(m\angle LMN = 116\), \(m\angle JKM=122\), and \(m\angle JNM = 103\). Let \(x=m\angle NKM\).

Step2: Set up the angle - sum equation

The sum of the angles around point K and in the relevant parts of the quadrilateral gives us the equation: \(m\angle JNM+m\angle LMN + m\angle JKM+x=360\).

Step3: Substitute the known values

Substitute \(m\angle JNM = 103\), \(m\angle LMN = 116\), and \(m\angle JKM = 122\) into the equation: \(103 + 116+122+x=360\).

Step4: Simplify the left - hand side

First, add the known angles on the left - hand side: \(103+116 + 122=341\). So the equation becomes \(341+x=360\).

Step5: Solve for \(x\)

Subtract 341 from both sides of the equation: \(x=360 - 341\).
\(x = 19\)

Answer:

19