Exercise 43 Page 292

Looking at the given diagram, we see that $\overline{LJ}\cong \overline{LK}.$ We also found that the measure of $\angle JLK=20^{\circ }$ in a previous exercise.

Now, we will remember the classification of triangles.

Classification of Triangles
Scalene Triangle	A scalene triangle is a triangle in which all three sides have different lengths.
Isosceles Triangle	An isosceles triangle is a triangle that has two congruent sides and two base angles with the same measure.
Equilateral Triangle	An equilateral triangle is a triangle in which all the sides are congruent.
Acute Triangle	An acute triangle is a triangle where all angles are less than $90^{\circ }$ or $\frac{\pi }{2}.$
Obtuse Triangle	An obtuse triangle is a triangle with exactly one an angle whose measure is greater than $90^{\circ }$ or $\frac{\pi }{2}.$
Right Triangle	A right triangle is a specific type of triangle that contains one angle of $90^{\circ }.$

Since the given triangle has two congruent sides, triangle $JKL$ is an isosceles triangle. We want to find $m\angle JKL.$ To do so, we will consider the Isosceles Triangle Theorem.

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

This means that $m\angle JKL=m\angle KJL.$ Then, we can use the Triangle Sum Theorem to calculate these missing angle measures. As a result, we found that $m\angle JKL=80.$