Chapter 12.1, Problem 54E

To determine

To find: the measurement of angle form by corner $KHL$ using the given diagram.

Answer to Problem 54E

  $m\angle KHL={43}^0.$

Explanation of Solution

Given:

  

Concept used:

The angles that have same measure is called congruence.

The angle of two unknown can be measured by equating the angles.

Calculation:

On the diagram it is clearly seen that the $\angle KHL\cong \angle LHG$ due to congruent angles.

  $\begin{array}{l}m\angle KHL\cong m\angle LHG.\\ 3x+1=5x-27.\\ 3x-5x=-28.\\ x=14.\end{array}$

By putting the value of $x$ in the given angle:

  $m\angle KHL=3x+1=3\left(14\right)+1={43}^0.$

Hence, $m\angle KHL={43}^0.$