Given: kl ║ nm , lm = 45, m∠m = 50° kn ⊥ nm , nl ⊥ lm find: kn and kl

Step-by-step explanation:

Given:

KL ║ NM ,

LM = 45

m∠M = 50°

KN ⊥ NM  

NL ⊥ LM

Find: KN and KL

1. Consider triangle NLM. This is a right triangle, because NL ⊥ LM. In this triangle,

LM = 45

m∠M = 50°

So,

Also

(angles LNM and M are complementary).

2. Consider triangle NKL. This is a right triangle, because KN ⊥ NM . In this triangle,

(alternate interior angles)

(angles KNL and KLN are complementary).

So,

and