Question

The adjacent angles of a parallelogram are in the ratio 5:7, the angles measure *​

Answer 1

Given

• The adjacent angles of a parallelogram are in the ratio 5:7.

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To find

• Measures of the angles.

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Solution

• Let the ratio be x.

Then,

→ First angle = 5x

→ Second angle = 7x

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• In a parallelogram, sum adjacent angles is 180°.

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⠀⠀⠀⠀⠀⠀⠀⠀⠀Therefore

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$\tt:\implies\: \: \: \: \: \: \: \: {5x + 7x = 180°}$

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$\tt:\implies\: \: \: \: \: \: \: \: {12x = 180}$

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$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{180}{12}}$

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$\bf:\implies\: \: \: \: \: \: \: \: {x = 15}$

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⠀⠀⠀By putting the value of x

$\tt\longmapsto{First\: angle = 5x = 75°}$

$\tt\longmapsto{Second\: angle = 7x = 105°}$

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Hence,

• The measures of the two angles are 75° and 105°.

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Answer 2

★Required AnswEr:

• The required measure of the angles are 75° and 105°.

★ Given Information:

• The adjacent angles of a parallelogram are in the ratio = 5:7

★ Need To Find:

• The required measure of the angles = ?

★Required Solution:

Let the first angle be 5y.

And the second angle be 7y.

★As we know that:

In Parallelogram,

• The sum of any two adjacent angles of a parallelogram is 180°.

★ According to the problem:

=> 5y + 7y = 180°

=> 12y = 180°

=> y = 180/12

=> y = 90/6

=> y = 30/2

=> y = 15°

★So,

• The required value of y is 15°.

★ Therefore:

• The First angle = 5y
• The First angle = 5 × 15
• The First angle = 75°

• The Second angle = 7y
• The Second angle = 7 × 15
• The Second angle = 105°

★ Hence:

• The required measure of the angles are 75° and 105°.