If the angles of a quadrilateral, taken in order, are in the ratio 1 : 2 : 3 : 4, prove that it is a trapezium.

Let a trapezium be ABCD. Let angles be x, 2x, 3x and 4x taken in order. Sum of angles of quadrilateral = 360°. ∴ x + 2x + 3x + 4x = 360° ⇒ 10x = 360° ⇒ x = ⇒ x = 36°. ⇒ ∠A = x = 36°, ⇒ ∠B = 2x = 2(36°) = 72° ⇒ ∠C = 3x = 3(36°) = 108° ⇒ ∠D = 2x = 4(36°) = 144°. From figure, ∠A and ∠D are co-interior angles and their sum = 180° (36° + 144°). Sum of co-interior angles = 180°, which means AB and CD are parallel. Also, Opposite angles sum i.e. ∠A + ∠C = 36° + 108° = 144°, ∠B + ∠D = 72° + 144° = 216°. Since, the sum of opposite angles ≠ 180° (Property of trapezium). Hence, proved that ABCD is a trapezium.

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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If an angle of a parallelogram is two-thirds of its adjacent angle, find the angles of the parallelogram.

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In the figure (1) given below, ABCD is a parallelogram in which ∠DAB = 70°, ∠DBC = 80°. Calculate angles CDB and ADB.

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In figure (2) given below, ABCD is a parallelogram. Find the angles of △AOD.

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Mathematics

If the angles of a quadrilateral, taken in order, are in the ratio 1 : 2 : 3 : 4, prove that it is a trapezium.

Rectilinear Figures

Related Questions

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

If an angle of a parallelogram is two-thirds of its adjacent angle, find the angles of the parallelogram.

In the figure (1) given below, ABCD is a parallelogram in which ∠DAB = 70°, ∠DBC = 80°. Calculate angles CDB and ADB.

In figure (2) given below, ABCD is a parallelogram. Find the angles of △AOD.