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Mathematics

Three angles of a quadrilateral are in the ratio 4 : 5 : 6. The sum of the least and the greatest of these angles is 160°. Find all the angles of the quadrilateral.

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Answer

It is given that the angles of a quadrilateral are in the ratio 4 : 5 : 6.

Let the three angles of the quadrilateral be 4a, 5a and 6a.

The sum of the least and the greatest of these angles is 160°.

Largest angle = 6a

Smallest angle = 4a

So,

⇒ 6a + 4a = 160°

⇒ 10a = 160°

⇒ a = 160°10\dfrac{160°}{10}

⇒ a = 16°

The three angles are 4a, 5a and 6a

⇒ 4 x 16°, 5 x 16° and 6 x 16°

⇒ 64°, 80° and 96°

As we know, the sum of all angles of quadrilateral is 360°.

⇒ 64° + 80° + 96° + x° = 360°

⇒ 240° + x° = 360°

⇒ x° = 360° - 240°

⇒ x° = 120°

Hence, the angles are 64°, 80°, 96° and 120°.

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