Question

The Ratio of the angles of a quadrilateral is 3: 5: 9: 13, find all the angles of this quadrilateral.​

Answer 1

Answer:

The ratio of the four angles of the quadrilateral is 36: 60: 108: 156. Dividing by 12, we can simplify the ratio as 3: 5: 9: 13. This is the ratio given in the question. Hence, we have verified the answer.

Answer 2

❍  Given that, the Ratio of the angles of a quadrilateral is 3: 5: 9: 13 and we need to  find all the angles of this quadrilateral.​

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Let's say that, the angles are -

∠A = 3x°

∠B = 5x°

∠C = 9x°

∠D = 13x°

As we know that,

• According to the angle sum property of quadrilaterals, sum of all angles of a quadrilateral is 360°

T H E R E F O R E,

⤳ ∠A + ∠B + ∠C + ∠D = 360°

⤳ 3x° + 5x° + 9x° + 13x° = 360°

⤳ 30x° = 360°

⤳ x = 360°/30

⤳ x = 36°/3

⤳ x = 12°

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Finding all angles :-

• By substituting the value of x in the values given to us

→ ∠A = 3x° = ( 3 × 12 )° = 36°

→ ∠B = 5x° = ( 5 × 12 )° = 60°

→ ∠C = 9x° = ( 9 × 12 )° = 108°

→ ∠D = 13x° = ( 13 × 12 )° = 156°