Question

The figure below is an iscoceles trapezoid. If m

Answer 1

..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

`m\angle M\cong m\angle L`

The upper base angles are congruent. The upper base angles are

`m\angle J\cong m\angle K`

Any lower base angle is supplementary to any upper base angle. This means that

`\begin{gathered} m\angle J+m\angle M=180^0 \\ m\angle K+m\angle L=180^0 \end{gathered}`
`\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}`

Also,

`\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}`
`\begin{gathered} m\angle L\cong m\angle M,m\angle L=119^0 \\ Therefore\colon \\ m\angle M=119^0 \end{gathered}`

Hence

m∠J = 61⁰

m∠L = 119⁰

m∠M = 119⁰