Question

m∠lnp is 90 degrees, which helps you determine the value of x since ∠jnk = 180 degrees. 5 if \\(\overrightarrow{np} \perp \overleftrightarrow{lm}\\), find \\(m\angle jnm\\). a) \\(129^\circ\\) memorial day b) \\(131^\circ\\) new year’s eve c) \\(134^\circ\\) mother’s day d) \\(138^\circ\\) mardi gras e) \\(141^\circ\\) thanksgiving

Explanation:

Step1: Set up equation for right angle

$\angle LNP = (13x-23)^\circ + (9x+3)^\circ = 90^\circ$

Step2: Simplify and solve for $x$

$22x - 20 = 90 \implies 22x = 110 \implies x = 5$

Step3: Calculate $\angle JNK$ (supplementary pair)

$\angle JNK = 180^\circ - (13x-23)^\circ$
Substitute $x=5$: $180 - (65-23) = 180 - 42 = 138^\circ$

Step4: Identify $\angle JNM = \angle JNK$

Vertical angles are equal, so $m\angle JNM = 138^\circ$

Answer:

D) $138^\circ$ Mardi Gras