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In parallelogram KLMN, KN = 10, MN = 7 and mK = 50°


a.Find the measures of the remaining angles of parallelogram KLMN. Justify each of the measures with a theorem.
b.Find the measures of the remaining side lengths of parallelogram KLMN. Justify each of the measures with a theorem.

In parallelogram KLMN KN 10 MN 7 and mK 50 aFind the measures of the remaining angles of parallelogram KLMN Justify each of the measures with a theorem bFind th class=

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Procrastinator467
a- 130, 130, and 50
b- 7 and 10
calculista

Answer:

Part A)

[tex]m<L=130\°[/tex]

[tex]m<M=50\°[/tex]

[tex]m<N=130\°[/tex]

Part B)

[tex]KL=7\ units[/tex]

[tex]LM=10\ units[/tex]

Step-by-step explanation:

we know that

In a parallelogram, the opposite angles and opposite sides are congruent, and consecutive angles are supplementary

Part A)

we know that

[tex]m<K=m<M[/tex] ----> by opposite angles

[tex]m<L=m<N[/tex] ----> by opposite angles

[tex]m<K+m<L=180\°[/tex] -----> by consecutive angles

we have

[tex]m<K=50\°[/tex]

Find the value of m<L

[tex]50\°+m<L=180\°[/tex]

[tex]m<L=180\°-50\°=130\°[/tex]

therefore

[tex]m<N=m<L=130\°[/tex]

[tex]m<M=m<K=50\°[/tex]

Part B)

we know that

[tex]KN=LM[/tex] ----> by opposite sides

[tex]KL=NM[/tex] ----> by opposite sides

we have

[tex]KN=10\ units[/tex]

[tex]NM=7\ units[/tex]

therefore

[tex]KL=7\ units[/tex]

[tex]LM=10\ units[/tex]

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