Question

look at this diagram:
if \\( \overleftrightarrow { g i } \\) and \\( \overleftrightarrow { j l } \\) are parallel lines and \\( m \angle l k m = 62 ^ { \circ } \\), what is \\( m \angle j k m \\)?

Explanation:

Step1: Recognize the relationship between angles

\(\angle LKM\) and \(\angle JKM\) are supplementary angles (they form a linear - pair).

Step2: Use the supplementary - angle formula

If two angles \(\alpha\) and \(\beta\) are supplementary, then \(\alpha+\beta = 180^{\circ}\). Let \(\alpha=\angle LKM = 62^{\circ}\) and \(\beta=\angle JKM\). So, \(m\angle LKM+m\angle JKM=180^{\circ}\).

Step3: Solve for \(m\angle JKM\)

Substitute \(m\angle LKM = 62^{\circ}\) into the equation \(m\angle LKM+m\angle JKM=180^{\circ}\). Then \(m\angle JKM=180^{\circ}-m\angle LKM\).

$$m\angle JKM = 180^{\circ}- 62^{\circ}$$

$$m\angle JKM=118^{\circ}$$

Answer:

\(118\)