Question

If the angles of a quadrilateral are in the ratio 3:5:7:9 . Then find the measure of the angles of quadrilateral ​

Answer 1

GIVEN :-

• Ratio of angles of a quadrilateral = 3 : 5 : 7 : 9

TO FIND :-

• The Measures of angles of the given quadilateral

SOLUTION :-

Let the ratio constant be x. Then the angles of the quadrilateral becomes " 3x " , " 5x " , " 7x " and 9x.

$\\ \star \: \boxed{\sf{\purple{Sum\:of\:all\:angles\:in\:quadrilateral=360^{\circ}}}}$

$\\ : \implies \sf \: 3x + 5x + 7x + 9x = 360$

$\\ : \implies \sf \: 24x = 360$

$\\ : \implies \sf \: x = \frac{360}{24}$

$\\ : \implies \boxed{\red{\mathfrak{\: x = 15 }}}$

Then the angles of the quadraliteral are ,

• 3x = 3(15) = 45°
• 5x = 5(15) = 75°
• 7x = 7(15) = 105°
• 9x = 9(15) = 135°

Hence , The measures of the angles of the given quadrilateral are 45° , 75° , 105° and 135°.

Answer 2

Answer:

Given :-

• The angles of a quadrilateral are in the ratio of 3:5:7:9.

To Find :-

• What is the measure of the each angles in quadrilateral.

Solution :-

✦ First angle be 3x

✦ Second angle be 5x

✦ Third angle be 7x

✦ Fourth angle will be 9x

And, we know that,

❑ Sum of all quadrilateral angles = 360°

According to the question by using the formula we get,

⇒ 3x + 5x + 7x + 9x = 360°

⇒ 24x = 360°

⇒ x = $\sf\dfrac{\cancel{360°}}{\cancel{24}}$

➠ x = 15°

Hence, the required angles are :-

◩ First angle = 3x = 3 × 15 = 45°

◩ Second angle = 5x = 5 × 15 = 75°

◩ Third angle = 7x = 7 × 15 = 105°

◩ Fourth angle = 9x = 9 × 15 = 135°

∴ The four angles of quadrilateral is 45°, 75°, 105°, 135° respectively.

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