Question

5. If JKZM is a rhombus, MK = 30, NL = 13, and mZMKZ = 41°, find each measure. a) NK = e) mML = b) JL = 1) MZMLK' = c) KI = g) mZMNL - M d) mJKM = h) mZKL = You may need to round your answers to tenths. b) c) e) f) h)

Answer 1

Fisrt we can find the similar angles and sides so we know that:

`\begin{gathered} 2NL=JL \\ NK=(NL)/(2) \end{gathered}`

so we can replace like:

`\begin{gathered} JL=2\cdot13=26 \\ NK=(30)/(2)=15 \end{gathered}`

now we can find the distance KL with pithagoras so:

`KL=√(15^2+13^2)`

and we operate so:

`\begin{gathered} KL=\sqrt[]{225+169} \\ KL=\sqrt[]{394} \\ KL=19.8 \end{gathered}`

Now the angle JKM will be equal to the angle MKZ so

`\angle JKM=41`

Now the angle JML will be:

`\begin{gathered} \angle JML=\angle JKM+\angle MKZ \\ \angle JML=41+41 \\ \angle JML=82 \end{gathered}`

the angle MLK will be the complement of 82 on a triangle so:

`\begin{gathered} \angle MLK=180-82 \\ \angle MLK=98 \end{gathered}`

For MNL we know that the segmente MK is perpendicular to JL so the angle is:

`\angle MNL=90`

and KJL will be halve of the angle MLK so:

`\angle KJL=(98)/(2)=49`