Question

The angles of a quadrilateral are in the
ratio 3 5 7 9 find the angles​

Answer 1

Answer:

45°, 75°, 105° and 135°

Step-by-step explanation:

Let the ratio be 3x : 5x : 7x : 9x.

According to the angle sum property of quadrilateral, the sum of all four angles is 360°.

=> 3x + 5x + 7x + 9x = 360°

=> 24x = 360°

=> x = 360° ÷ 24

=> x = 15°

Therefore, first angle = (3×15)° = 45°

Second angle = (5×15)° = 75°

Third angle = (7×15)° = 105°

Fourth angle = (9×15)° = 135°

Answer 2

Given

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

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To Find

• The value of the angles

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Solution

We know the angle sum property of quadrilateral that the sum of all interior angles of a quadrilateral will always be 360°

So keeping that in mind we can say that,

∠1 → 3x

∠2 → 5x

∠3 → 7x

∠4 → 9x

[We have taken these values of angles because they are in a ratio of 3:5:7:9]

Now let's solve this equation to find the value of 'x'.

3x + 5x + 7x + 9x = 360

Step 1: Simplify the equation.

⇒ 3x + 5x + 7x + 9x = 360

⇒ 24x = 360

Step 2: Divide 24 to both sides of the equation.

⇒ 24x ÷ 24 = 360 ÷ 24

⇒ x = 15

∴ The value of 'x' is 15.

With the obtained value of 'x', we will substitute it to the value of angles we had determined earlier.

→ ∠1 = 3x = 3(15) = 45°

→ ∠2 = 5x = 5(15) = 75°

→ ∠3 = 7x = 7(15) = 105°

→ ∠4 = 9x = 9(15) = 135°

Let's verify if the values of angles obtained are giving the sum 360.

⇒ ∠1 + ∠2 + ∠3 + ∠4

⇒ 45 + 75 + 105 + 135

⇒ 360

∴ The values of the angles are 45°, 75°, 105° and 135°

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