Question

Given: LM ∥ KN LP ⊥ KN , KL = MN KN = 30, LM = 20 m∠KLM=126° Find: LP

Answer 1

An angle is produced at the point where two or more lines meet. Thus the value of LP required in the question is approximately 14.

Two lines are said to be perpendicular when a measure of the angle between them is a right angle. While parallel lines are lines that do not meet even when extended to infinity.

From the question, let the length of LP be represented by x.

Thus, from the given question, it can be deduced that;

LM ≅ PN = 20

KP = KN - PN

    = 30 - 20

KP = 10

LP = x

Also,

<MLP is a right angle, so that;

< KLP = < KLM - <PLM

         = 126 - 90

<KLP = $36^{o}$

So that applying the Pythagoras theorem to triangle KLP, we have;

Tan θ = $\frac{opposite}{adjacent}$

Tan 36 = $\frac{10}{x}$

x = $\frac{10}{Tan 36}$

  = $\frac{10}{0.7265}$

x = 13.765

Therefore the side LP ≅ 14.

For more clarifications on segments and angles, visit: brainly.com/question/4976881

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