Question

The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.​

Answer 1

$\huge\underline\mathrm{SOLUTION:-}$

Let the common ratio between the angles be = x.

We know that the sum of the interior angles of the quadrilateral = 360°

Now,

3x + 5x + 9x + 13x = 360°

➠ 30x = 360°

➠ x = 12°

Angles of the quadrilateral are:

3x = 3 × 12° = 36°

5x = 5 × 12° = 60°

9x = 9 × 12° = 108°

13x = 13 × 12° = 156°

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Answer 2

$\bold{Given : }$

The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13.

$\bold{To \: find \: out : }$

Find all the angles of the quadrilateral?

$\bold{Solution : }$

We have,

∠A : ∠B : ∠C : ∠D = 3 : 5 : 9 : 13

So,

Let ∠A = 3x°

∠B = 5x°

∠C = 9x°

∠D = 13x°

We know that,

Sum of all angles of a quadrilateral = 360°

→ ∠A + ∠B + ∠C + ∠D = 360°

→ 3x + 5x + 9x + 13x = 360°

→ 17x + 13x = 360°

→ 30x = 360°

→ x = 360/30

→ x = 12

Thus, the angles are

∠A = 3x = 3 × 12 = 36°

∠B = 5x = 5 × 12 = 60°

∠C = 9x = 9 × 12 = 108°

∠D = 13x = 13 × 12 = 146°