Question

Ina quadrilateral the angle A,B,C and D are in the ratio 1:2:3:4. Find the measure of each angle of the quadrilateral​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

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

Step-by-step-explanation:

The angles of a quadrilateral A, B, C & D are in the ratio 1 : 2 : 3 : 4.

Let the common multiple be x.

∴ The angles are x, 2x, 3x & 4x.

We know that,

The sum of measures of angles of a quadrilateral is 360°.

⇒ A + B + C + D = 360°

⇒ x + 2x + 3x + 4x = 360

⇒ 3x + 7x = 360

⇒ 10x = 360

⇒ x = 360 ÷ 10

⇒ x = 36°

Now, the angles are

Angle A = x = 36°

Angle B = 2x = 2 * 36 = 72°

Angle C = 3x = 3 * 36 = 108°

Angle D = 4x = 4 * 36 = 144°

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