1 Answer

Milap · Answer 1 · 2023-03-15T11:12:32+0000

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

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