Question

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

Answer 1

36°,72°,108° and 144° respectively.

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Answer 2

Given:-

• Ratios of angles of a quadrilateral = 1:2:3:4

To find:-

• Measure of all four angles.

Assumption:-

• Let the common factor be x
• 1st angle = 1x
• 2nd angle = 2x
• 3rd angle = 3x
• 4th angle = 4x

Solution:-

According to the angle sum property of the quadrilateral, The sum of all angles of a quadrilateral is 360⁰.

= 1x + 2x + 3x + 4x = 360⁰

=> 3x + 7x = 360⁰

=> 10x = 360⁰

=> x = 360⁰/10

=> x = 36⁰

Measure of each angles:-

• 1st angle = 1x = 1×36⁰ = 36⁰
• 2nd angle = 2x = 2×36⁰ = 72⁰
• 3rd angle = 3x = 3×36⁰ = 108⁰
• 4th angle = 4x = 4×36⁰ = 144⁰

Verification:-

Sum of measures of each angle of the quadrilateral must be 360⁰

= 36⁰ + 72⁰ + 108⁰ + 144⁰

= 108⁰ + 252⁰

= 360⁰

[Hence verified].