Question

The rhombus below NL=3, KL=5, and angle JML=60°Find angle KLM

Answer 1

A rhombus has certain characteristics that will be of use in this problem:

• All interior angles add up to 360.

,

• Opposite angles are congruent.

Based on the latter, we can build the following conclusions:

`m\angle JLM=m\angle JKL`
`m\angle KLM=m\angle KJM`
`m\angle JLM+m\angle JKL+m\angle KLM+m\angle KJM=360`

As m∠JLM is given, and as opposite angles measure the same, we can do the following:

`2\cdot(m\angle JLM)+2\cdot(m\angle KLM)=360`
`2\cdot(60)+2\cdot(m\angle KLM)=360`
`120+2\cdot(m\angle KLM)=360`

Solving for m∠KLM:

`2\cdot(m\angle KLM)=360-120`
`2\cdot(m\angle KLM)=240`
`m\angle KLM=(240)/(2)`
`m\angle KLM=120`

Answer: a. 120