Question

The angles of a quandrilateral are in the ratio 1 : 2 : 3 : 4 .What are the measures of the four angles..?​

Answer 1

Answer:

Given the ratio of the Angles of quadrilateral = 1 : 2 : 3 : 4

Therefore, let the Angles of quadrilateral be x , 2x , 3x , 4x

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We know that,

Sum of all angles of a quadrilateral is 360°

: $\implies$ x + 2x + 3x + 4x = 360°

: $\implies$ 10x = 360°

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

: $\implies$ x = $\boxed{\sf{36°}}$

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Measures of angles :-

x = 36°

2x = 2 × 36 = 72°

3x = 3 × 36 = 108°

4x = 4 × 36 = 144°

Answer 2

|| SOLUTION ||

Question:

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

Given:

The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4.

To Find:

The angles of the quadrilateral

Answer:

36°

72°

108°

144°

Step-By-Step-Explanation:

Let the angles of the quadrilateral be 1x , 2x , 3x and 4x.

Sum of the angles

= 1x + 2x + 3x + 4x

= 10x

But sum of all the angles of a quadrilateral is 360°

Therefore,

10x = 360°

=> x = 360°/10

=> x = 36°

Therefore,

The angles are :-

1x = 1 * 36° = 36°

2x = 2 * 36° = 72°

3x = 3 * 36° = 108°

4x = 4 * 36° = 144°