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garri49 [273]
3 years ago
10

If each quadrilateral below is a parallelogram,find the missing measures.

Mathematics
1 answer:
zhenek [66]3 years ago
7 0

Answer:

Part 1) MN=31\ units

Part 2) KN=45\ units

Part 3) m∠K=61°

Part 4) m∠L=119°

Part 5) m∠M=61°

Step-by-step explanation:

we know that

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

Part 1) Find the side MN

we know that

MN≅KL ----> by opposite sides

we have

KL=31\ units

therefore

MN=31\ units

Part 2) Find the side KN

we know that

KN≅LM ----> by opposite sides

we have

LM=45\ units

therefore

KN=45\ units

Part 3) Find the measure of angle K

we know that

m∠K+m∠N=180° ----> by consecutive interior angles

we have

m∠N=119°

substitute

m∠K+119°=180°

m∠K=180°-119°

m∠K=61°

Part 4) Find the measure of angle L

we know that

m∠L≅m∠N ----> by opposite angles

we have

m∠N=119°

therefore

m∠L=119°

Part 5) Find the measure of angle M

we know that

m∠M≅m∠K ----> by opposite angles

we have

m∠K=61°

therefore

m∠M=61°

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