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3 years ago

A mural inspired by photo graph measures 107 inches by 180 inches.the scale factor is 12.what are the dimensions of the photogra

1 answer:

5 0

$\bf \cfrac{mural}{photo}\qquad \cfrac{12}{1}\implies \stackrel{mural}{12}:\stackrel{photo}{1}\qquad \qquad \cfrac{\stackrel{width}{107}}{w}=\cfrac{12}{1}\implies \cfrac{107\cdot 1}{12}=w
\\\\\\
\cfrac{\stackrel{height}{180}}{h}=\cfrac{12}{1}\implies \cfrac{180\cdot 1}{12}=h$

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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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