Question

the four angle of quadrilateral are in the ratio 3 5 7 9 find the angle​

Answer 1

$\sf{\huge{\underline{\green{Given :-}}}}$

• The four angle of quadrilateral are in the ratio 3 : 5 : 7 : 9 .

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• All the angles of quadrilateral.

$\sf{\huge{\underline{\green{Answer :-}}}}$

According to the question,

The four angle of quadrilateral are in the ratio 3 : 5 : 7 : 9 .

Let the angles be in form of x,

Such that 3x, 5x, 7x & 9x.

We know that, the sum of all angles of a quadrilateral is 360°.

∠A + ∠B + ∠C + ∠D = 360°

➝ 3x + 5x + 7x + 9x = 360°

➝ 8x + 16x = 360°

➝ 24 x = 360°

➝ x = 360°/ 24

➝ x = 15°

∠A = 3x = 3× 15 = 45°

∠B = 5x = 5 × 15 = 75°

∠C = 7x = 7 × 15 = 105°

∠D = 9x = 9 × 15 = 135°

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Answer 2

Question :-

The four angles of quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the measure of each angle.

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Solution :-

➲ Given Information :-

• Figure ➢ Quadrilateral
• Ratio of angles ➢ 3 : 5 : 7 : 9

➲ To Find :-

• The measure of each angle of the Quadrilateral

➲ Formula Used :-

• Sum of all the angles of a Quadrilateral = 360°

➲ Concept :-

Quadrilaterals

➲ Explanation :-

The four angle of quadrilateral are in the ratio 3 : 5 : 7 : 9. We will take common factor as 'x'. Then equate the equation to find the value of 'x'. The value of 'x' will be multiplied with each term of the ratio provided and get the measure of each angle of the Quadrilateral.

➲ Calculation :-

The four angle of quadrilateral are in the ratio 3 : 5 : 7 : 9.

Let the common factor of the angles be 'x',

⇒ Angles of the Quadrilateral = 3x, 5x, 7x & 9x

∵ The figure is a Quadrilateral, We will use the above mentioned formula.

⇒ The sum of all angles of a quadrilateral = 360°

⇒ ∠A + ∠B + ∠C + ∠D = 360°

Substituting the values given, We get,

⇒ 3x + 5x + 7x + 9x = 360°

⇒ 12x + 12x = 360°

⇒ 24x = 360°

Transposing 24 to Right Hand Side of the equation, We get,

⇒ x = $\sf{ \dfrac{360°}{24} }$

Cancelling & Calculating further, We get,

⇒ x = 15°

∴ Substituting the value of 'x' in the value of angles and equating to get the measure of each angle,

⇒ ∠A = 3x = 3 × 15 = 45°

⇒ ∠B = 5x = 5 × 15 = 75°

⇒ ∠C = 7x = 7 × 15 = 105°

⇒ ∠D = 9x = 9 × 15 = 135°

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Final Answers :-

• Measure of ∠A = 45°
• Measure of ∠B = 75°
• Measure of ∠C = 105°
• Measure of ∠D = 135°

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