Question

the angles of a quadrilateral in the ratio 1:2:3:4 .find the smallest and the largest angle

Answer 1

let the angles be x, 2x, 3x ,4x....

x + 2x +3x + 4x =360°
10x = 360 °
x = 36

smallest angle = 36°
largest angle =4x =4×36
=144°

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Answer 2

Given, angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4

Let the constant be x

Let the 1st angle be x, 2nd be 2x, 3rd be 3x and 4th be 4x

The sum of all angles of a quadrilateral is 360°

According to the question,

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

➾ 10x = 360

➾ x = $\dfrac{360}{10}$

➾ x = 36


∴ 1st angle ➾ x

➾ $\red{\boxed{\blue{36^{\circ}}}}$


∴ 2nd angle ➾ 2x

➾ 2 × 36

➾ $\red{\boxed{\blue{72^{\circ}}}}$


∴ 3rd angle ➾ 3x

➾ 3 × 36

➾ $\red{\boxed{\blue{108^{\circ}}}}$


∴ 4th angle ➾ 4x

➾ 4 × 36

➾ $\red{\boxed{\blue{144^{\circ}}}}$




∴ The smallest angle is 36° and the biggest angle is 144°