Question

a quadrilateral name ABCD. if the angles of A, B, C and D are in ratio of 2:4:5:7 . find the measure of each angle of the quadrilateral​

Answer 1

Answer:

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Answer 2

★ AnswEr:-

• ∠A = 40°
• ∠B = 80°
• ∠C = 100°
• ∠D = 140°

★ GivEn :-

• ABCD is a quadrilateral and the angles are in the ratio of 2:4:5:7.

★ To Find :-

• The measures of each angle of the quadrilateral.

★ Solution :-

We know that, the sum of four angles of a quadrilateral is 360°

Let the common factor of the ratio be x.

Therefore,

• ∠A = 2x°
• ∠B = 4x°
• ∠C = 5x°
• ∠D = 7x°

2x° + 4x° + 5x° + 7x° = 360°

or, 18x° = 360°

or, x = 360° ÷ 18°

or, x = 20

Now, putting the value of the common factor (x) in the place of the ratio of each angles we get,

• ∠A = 2° × 20 = 40°
• ∠B = 4° × 20 = 80°
• ∠C = 5° × 20 = 100°
• ∠D = 7° × 20 = 140°

• We can verify the answers by adding the values of the angles we have got in the solution.

40° + 80° + 100° + 140° = 360°

• Therefore, the calculation is verified.