Question

the four angles of a quadrilateral are in the ratio 1:2:3:4. find their measurements

Answer 1

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

We know that sum of all measures of a quadrilateral is 360°


According to the question,

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

10x = 360

x = $\dfrac{360}{10}$

x = 36



1st angle's measure is x

=> 36°

2nd angle's measure is 2x

=> 2 × 36

=> 72°

3rd angle's measure is 3x

=> 3 × 36

=> 108°

4th angle's measure is 4x

=> 4 × 36

=> 144°

Answer 2

Let the 1st angle be 1x
Let the 2nd angle be 2x
Let the 3rd angle be 3x
Let the 4th angle be 4x
Sum of all the angles of a quadrilateral = 360°

1x + 2x + 3x + 4x = 360°
10x = 360 °
x = 360°/10
x = 36

1x = 1×36 = 36°
2x = 2×36 = 72°
3x = 3×36 = 108°
4x = 4×36 = 144°

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