Question

10. Three angles of a quadrilateral are in the ratio 1:2:3. The sum of the least and
the greatest of these angles is 200°. Find all the four angles of the quadrilatera
​

Answer 1

Given :-

• Ratio of angles of quadrilateral :-
• 1 : 2 : 3
• Sum of least and greatest angles - 200°

To Find :-

• All four angles

Solution :-

Let the angles be - 1x, 2x and 3x

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Least angle = 1x

Greatest angle = 3x

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Sum of least and greatest angle is 200

--------------

Therefore,

1x + 3x = 200

4x = 200

x = 200/4

x = 50

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Finding all angles :-

1x = 1 (50) = 50°

2x = 2 (50) = 100°

3x = 3 (50) = 150°

Fourth angle = 360 - (50+100+150) = 360 - 300

= 60°

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Angles are, 50°, 100°, 150° and 60°

Answer 2

Answer :

The four angles of a quadrilateral are 50°, 100°, 150° and 60°.

Explanation :

The ratio of the three angles of quadrilateral = 1 : 2 : 3

Let, the angles be x, 2x and 3x.

The greatest angle among these is 3x and the least is x.

According to the question,

x + 3x = 200

=> 4x = 200

=> x = 200/4

=> x = 50

Hence, the three angles of quadrilateral are

x = 50°

2x = 2 × 50 = 100°

3x = 3 × 50 = 150°

Fourth angle of quadrilateral

= 360° - sum of three angles

= 360 - (50° + 100° + 150°)

= 360° - 300°

= 60°

Thus, the four angles of a quadrilateral are 50°, 100°, 150° and 60°.

Verification :

Sum of all four angles of a quadrilateral = 360°

=> (50° + 100° + 150° + 60°) = 360°

=> 360° = 360°

Hence, it's verified.......