Question

if \\( \overrightarrow { n p } \perp \overrightarrow { l m } \\), find \\( m \angle j n m \\).

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(13x - 23=9x + 3\)

$$
LATEXBLOCK0
$$

Step2: Find \(m\angle JNL\)

Substitute \(x = 7\) into \(13x-23\): \(13\times7-23=91 - 23=68^{\circ}\)

Step3: Use the linear - pair property

Since \(\overrightarrow{NP}\perp\overrightarrow{LM}\), \(\angle LNP = 90^{\circ}\). And \(\angle JNM+\angle LNP+\angle JNL=180^{\circ}\) (a straight line measures \(180^{\circ}\))
\(\angle JNM=180^{\circ}-\angle LNP-\angle JNL\)
Substitute \(\angle LNP = 90^{\circ}\) and \(\angle JNL = 68^{\circ}\)
\(\angle JNM=180 - 90-68=131^{\circ}\)

Answer:

\(131\) degrees