Question

ratio of consective angles of a quadrilateral is 1:2:3:4 find the measure of its each angle write with reason what type of quadrilateral it is​

Answer 1

Let PQRS be the quadrilateral.

Ratio of consecutive angles of a quadrilateral is 1 : 2 : 3 : 4.

Let the common multiple be x.

∴ m∠P = x°, m∠Q = 2x°,

m∠R = 3x° and m∠S = 4x°

In PQRS, m∠P + m∠Q + m∠R + m∠S = 360°

…[Sum of the measures of the angles of a quadrilateral is 360°]

∴ x° + 2x° + 3x° + 4x° = 360°

∴10 x° = 360°

∴ x° = 360/10

∴ x° = 36°

∴ m∠P = x° = 36° m∠Q = 2x° = 2 × 36° = 72°

m∠R = 3x° = 3 × 36° = 108° and

m∠S = 4x° = 4 × 36° = 144°

∴ The measures of the angles of the quadrilateral are 36°, 72°, 108°, 144°.

Here, m∠P + m∠S = 36° + 144° = 180° Since, interior angles are supplementary,

∴ side PQ || side SR m∠P + m∠Q = 36° + 72° = 108° ≠ 180°

∴ side PS is not parallel to side QR. Since, one pair of opposite sides of the given quadrilateral is parallel.

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