..Given an isosceles trapezoid
The following are the properties of an isosceles trapezoid
The legs are congruent by definition (From the diagram, the legs are JM and KL)
The lower base angles are congruent. The lower base angles are
[tex]m\angle M\cong m\angle L[/tex]
The upper base angles are congruent. The upper base angles are
[tex]m\angle J\cong m\angle K[/tex]
Any lower base angle is supplementary to any upper base angle. This means that
[tex]\begin{gathered} m\angle J+m\angle M=180^0 \\ m\angle K+m\angle L=180^0 \end{gathered}[/tex][tex]\begin{gathered} \text{If} \\ m\angle K=61^0 \\ \text{Therefore} \\ m\angle J\cong m\angle K=61^0 \\ m\angle J=61^0 \end{gathered}[/tex]
Also,
[tex]\begin{gathered} m\angle L+m\angle K=180^0 \\ m\angle L+61^0=180^0 \\ m\angle L=180^0-61^0 \\ m\angle L=119^0 \end{gathered}[/tex][tex]\begin{gathered} m\angle L\cong m\angle M,m\angle L=119^0 \\ Therefore\colon \\ m\angle M=119^0 \end{gathered}[/tex]
Hence
m∠J = 61⁰
m∠L = 119⁰
m∠M = 119⁰
