Question

if np ⊥ lm, find m∠jnm. (13x - 23)° (9x + 3)° a) 129° b) 131° c) 134° d) 138° e) 141° memorial day new year’s eve mother’s day mardi gras thanksgiving

Explanation:

Answer:

1. First, since \(\overrightarrow{NP}\perp\overrightarrow{LM}\), then \(\angle LNP = 90^{\circ}\).

• We know that \(\angle JNL=(13x - 23)^{\circ}\) and \(\angle PNK=(9x + 3)^{\circ}\), and \(\angle JNL+\angle LNP+\angle PNK = 180^{\circ}\) (a straight - line angle).
• Substitute \(\angle LNP = 90^{\circ}\) into the equation: \((13x - 23)+90+(9x + 3)=180\).
• Combine like terms: \(13x+9x-23 + 3+90=180\), which simplifies to \(22x+70 = 180\).
• Subtract 70 from both sides: \(22x=180 - 70=110\).
• Divide both sides by 22: \(x = 5\).

1. Then find \(\angle JNL\):

• Substitute \(x = 5\) into the expression for \(\angle JNL\): \(\angle JNL=13x-23=13\times5 - 23=65 - 23 = 42^{\circ}\).

1. Finally, find \(\angle JNM\):

• \(\angle JNM = 180^{\circ}-\angle JNL\).
• Substitute \(\angle JNL = 42^{\circ}\): \(\angle JNM=180 - 42=138^{\circ}\).

So the answer is D. 138°