Mathematics

If two angles of a quadrilateral are 40° and 110° and the other two are in the ratio 3 : 4, find these angles.

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Sum of angles of quadrilateral = 360°.

Let other two angles be 3x and 4x.

∴ 3x + 4x + 40° + 110° = 360°

⇒ 7x + 150° = 360°

⇒ 7x = 360° - 150°

⇒ 7x = 210°

⇒ x = $\dfrac{210°}{7}$

⇒ x = 30°

⇒ 3x = 3(30°) = 90° and 4x = 4(30°) = 120°.

Hence, other two angles are 90° and 120°.

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