Question

find the measures of the four angles of a quadrilateral if they are in the ratio 2:4:6:8.​

Answer 1

Answer:

The ratio of the angles is 2:3:4:6

To find: The measures of each angle.

Observe that 2+3+4+6=15.

Thus 15 parts accounts for 360  

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Hence, 15 parts = 360  

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2 parts = ( 360  

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/15)×  2 = 48  

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3 parts = (360  

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/15)× 3 = 72  

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4 parts = ( 360  

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 /15)×  4 = 96  

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6 parts = ( 360  

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/15)× 6 = 144  

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Thus the angles are 48  

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 72  

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, 96  

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 144  

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Step-by-step explanation:

Answer 2

✬ Angles = 36° , 72° , 108° , 144° ✬

Step-by-step explanation:

Given:

• Ratio of angles of quadrilateral are 2 : 4 : 6 : 8

To Find:

• What is the measure of each angle?

Solution: Let x be the common in given ratios. Therefore

➟ First angle = 2x

➟ Second angle = 4x

➟ Third angle = 6x

➟ Fourth angle = 8x

As we know that

★ Sum of all angles of Quadrilateral = 360° ★

A/q

$\implies{\rm }$ 1st + 2nd + 3rd + 4th = 360°

$\implies{\rm }$ 2x + 4x + 6x + 8x = 360

$\implies{\rm }$ 20x = 360

$\implies{\rm }$ x = 360/20

$\implies{\rm }$ x = 18°

So, angles are

➛ First = 2x = 2(18) = 36°

➛ Second = 4x = 4(18) = 72°

➛ Third = 6x = 6(18) = 108°

➛ Fourth = 8x = 8(18) = 144°

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★ Verification ★

➧ 36° + 72° + 108° + 144° = 360°

➧ 108° + 252° = 360°

➧ 360° = 360°

$\implies{\rm }$