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=\frac{240}{2}$$m\angle KLM=120$

Answer: a. 120