Question

an engineer is designing the parking - lot shown below for a local grocery store. the parking spaces are marked with the lines where xd || tz || yf || lp and wc is a transversal.
given:
∠xrh=(8x + 2)°
∠lnc=(10x - 14)°
part a: find the measures of each angle below.
m∠lnc=
m∠cnp=
part b: ∠fbn is ∠lnb

Explanation:

Step1: Set corresponding angles equal

$8x + 2 = 10x - 14$

Step2: Solve for x

$2x = 16 \implies x = 8$

Step3: Calculate m∠LNC

$10x - 14 = 10(8) - 14 = 66$

Step4: Find m∠CNP (supplementary to ∠LNC)

$180 - 66 = 114$

Step5: Identify ∠FBN and ∠LNB relationship

Alternate interior angles (YF || LP, transversal WC) are congruent.

Answer:

m∠LNC = 66°
m∠CNP = 114°
∠FBN is congruent to ∠LNB