If a trapezoid is isosceles, then each pair of base angles is congruent.
From the diagram we know that KJ and LM are parallel, so these are the bases of the trapezoid. This means ∠ J and ∠ K are base angles and congruent.
m∠ J= m∠ K
It is given that ∠ K measures 118^(∘). Therefore, ∠ J also measures 118^(∘).
m∠ J= 118^(∘)
Measure of ∠ M
Now let's add the measure of ∠ J to the diagram and analyze how we can find m∠ M.
Note that ∠ M and ∠ L are base angle of the isosceles trapezoid JKLM, so they are congruent. Earlier we have found that m∠ M=62^(∘), which allows us to conclude that ∠ L also measures 62^(∘).
