The angles of a quadrilateral are in the ratio 2: 4 : 5 : 7.

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Question:
The angles of a quadrilateral are in the ratio 2: 4 : 5 : 7. Find the angles.

Solution:

Let $∠ "> ∠$ A = 2x∘.
Then $∠ "> ∠$ B = (4x)∘; $∠ "> ∠$ C = (5x)∘ and $∠ "> ∠$ D = (7x)∘
Since the sum of the angles of a quadrilateral is 360o, we have:
2x + 4x + 5x + 7x = 360∘
⇒ 18 x = 360∘
⇒ x = 20∘
∴ $∠ "> ∠$ A = 40∘; $∠ "> ∠$ B = 80∘; $∠ "> ∠$ C = 100∘; $∠ "> ∠$ D = 140∘

The angles of a quadrilateral are in the ratio 2: 4 : 5 : 7.

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