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The angles of a quadrilateral are in the ratio of 1 : 2 : 3 : 4. What is the measure of the four angles?

 The angles of a quadrilateral are in the ratio of 1 : 2 : 3 : 4. What is the measure of the four angles?

 

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
11 months ago
Dear Student

The ratio of the angles of quadrilaterals = 1 : 2 : 3 : 4

Let the four angles of the quadrilateral be x, 2x, 3x, and 4x respectively.

The sum of four angles of a quadrilateral is 360°.

Therefore,

x + 2x + 3x + 4x = 360°

10x = 360°

x = 360°/10

x = 36°

Therefore,

First angle = x = 36°

Second angle = 2x = 2× 36 = 72°

Third angle = 3x = 3× 36 = 108°

Fourth angle = 4x = 4× 36 = 144°

Hence, the measure of four angles is 36°,72°, 108°and 144°.


Thanks

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