Question

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.

Answer 1

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

Answer 2

Part A)

`m<L=130\°`

`m<M=50\°`

`m<N=130\°`

Part B)

`KL=7\ units`

`LM=10\ units`

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

`m<K=m<M` ----> by opposite angles

`m<L=m<N` ----> by opposite angles

`m<K+m<L=180\°` -----> by consecutive angles

we have

`m<K=50\°`

Find the value of m<L

`50\°+m<L=180\°`

`m<L=180\°-50\°=130\°`

therefore

`m<N=m<L=130\°`

`m<M=m<K=50\°`

Part B)

we know that

`KN=LM` ----> by opposite sides

`KL=NM` ----> by opposite sides

we have

`KN=10\ units`

`NM=7\ units`

therefore

`KL=7\ units`

`LM=10\ units`