Question

The angles of a quadrilateral are in the ratio 2:3:4:1.Find the measure of the smallest and greatest angle

Answer 1

Answer: The smallest is 36° and the greatest is 144°

Step-by-step explanation:

Let the angles of quadrilateral be

2x, 3x, 4x, x

sum of all angles of quadrilateral = 360°

x + 2x + 3x + 4x = 360°

10x = 360°

x = 360/10 = 36°

the four angles are :-

x = 36°

2x = 2 × 36 = 72°

3x = 3 × 36 = 108°

4x = 4 × 36 = 144°

The smallest is 36° and the greatest is 144°

Answer 2

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

Sum of all angles of a quadrilateral is 360°

According to the given condition,

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

∴ 10x = 360

∴ x = 36

∴ 1st angle ➾ 2x

➾ 2 × 36

➾ 72°

∴ 2nd angle ➾ 3x

➾ 3 × 36

➾ 108°

∴ 3rd angle ➾ 4x

➾ 4 × 36

➾ 144°

∴ 4th angle ➾ x

➾ 36°


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