Chapter 5.6, Problem 38HP

To determine

To explain: Which angle is larger, $\angle LKN$ or $\angle LNK$ in the given diagram of quadrilateral.

Answer to Problem 38HP

  $m\angle LKN$ is greater.

Explanation of Solution

Given:Where $m\angle LJN>m\angle KJL,KJ\cong JN$ and $JN\perp NL$

  

$m\angle LJN>m\angle KJL,KJ\cong JN$ and $JN\perp NL$ is given and it has to explain which angle is larger $\angle LKN$ or $\angle LNK$ .

In triangle $\Delta JKL$ and $\Delta JNL$ it is given

  $m\angle LJN>m\angle KJL,KJ\cong JN$ and $JL\cong JL\left(\text{common}\right)$ .

Then the measure of the sides opposite $\angle LKN$ and $\angle LNK$ are related to as $LN>LK$ (by Hinge theorem).

Because $\angle LN>\angle LK$ , then $m\angle LKN>\angle LNK$ by angle side relationship in a triangle.

Hence $m\angle LKN$ is greater.