Question

The angles of a quadrilateral are in the ratio 1:2:34. Find the measure of four angles.​

Answer 1

Answer and Step-by-Step Explanation:

Question:-

The angles of a quadrilateral are in the ratio 1:2:3:4. Find the measure of four angles.​

Solution:-

⇒  Let the measure of angles be x, 2x, 3x and 4x.

We know that sum of measure of all four angles is 360°.  

∴  x + 2x + 3x + 4x = 360°  

 

⇒  10x = 360°  

 

⇒  x = 36°  

 

⇒  2x = 2 × 36° = 72°  

 

⇒  3x = 3 × 36°  = 108°  

 

⇒  4x = 4 × 36°   = 144°

⇒  The measures of angles of quadrilateral are 36°, 72°,  108° and 144°.

⇒ We can see measure of all 4 angles are different so, the given quadrilateral is trapezium.

Answer:

The measures of the angles of quadrilateral are 36°, 72°,  108° and 144°.

Answer 2

Given

• The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4

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To Find

• The measure of the four angles.

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Solution

Let the first angle be → x°

Second angle → 2x°

Third angle → 3x°

Fourth angle → 4x°

We know that, Sum of all angles in a quadrilateral is 360°

So let's solve the following equation to find each angle.

x + 2x + 3x + 4x = 360

Step 1: Simplify the equation.

⇒ x + 2x + 3x + 4x = 360

⇒ 10x = 360

Step 2: Divide 10 from both sides of the equation.

⇒ 10x ÷ 10 = 360 ÷ 10

⇒ x = 36

∴ ∠1 = x° = 36°

∴ ∠2 = 2x° = 2(36) = 72°

∴ ∠3 = 3x° = 3(36) = 108°

∴ ∠4 = 4x° =4(36) = 144°

∴ The measures of all four angles are 36°, 72°, 108° and 144°

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