Question

ration of consecutive angle of a quadrilateral 1:2:3:4. find the measure of a quadrila it is​

Answer 1

Answer:

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.

∴The given quadrilateral is a trapezium.

Answer 2

Answer:

x = 20

Step-by-step explanation:

$sum \: of \: all \: angles \: = 360 {}^{0} \\ 1x + 2x + 3x + 4x = 360 \\ 13 x = 360 \\ x = \frac{360}{13} \\ x = 20 \\ 1st \: angle = 20 \\ 2nd \: angle = 40 \\ 3rd \: angle = 60 \\ 4th \: angle = 80$

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