Question

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

Answer 1

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

Answer:

• The required angles of the quadrilateral are 36°, 60°, 108° and 156°.

Given:

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

Need To Find:

• All the angles of the quadrilateral = ?

Explanation:

Let the angles of the quadrilateral be 3x, 5x, 9x and 13x.

Therefore:

3x + 5x + 9x + 13x = 360°

[Angle sum property of a quadrilateral]

➠ 30x = 360°

➠ x = $\frac { { 360 }^{ \circ } }{ 30 }$= 12°

Therefore:

➠ 3x = 3 x 12° = 36°

➠ 5x = 5 x 12° = 60°

➠ 9x = 9 x 12° = 108°

➠ 13x = 13 x 12° = 156°

• The required angles of the quadrilateral are 36°, 60°, 108° and 156°.

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Answer 2

Given :

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

To find :

• All the angles of the quadrilateral = ?

Step-by-step explanation :

Let, The angles of quadrilateral are in the ratio 3x, 5x, 9x and 13x.

As we know that,

Sum of all angles of quadrilateral = 360°

So,

∠A + ∠B + ∠C + ∠D = 360°

Substituting the values, we get,

3x + 5x + 9x + 13 x = 360°

8x + 9x + 13x = 360°

17x + 13x = 360°

30x = 360°

x = 360°/30

x = 12°.

Therefore, We know that the value of x = 12°.

Hence,

∠A = 3x = 3 × 12° = 36°

∠B = 5x = 5 × 12° = 60°

∠C = 9x = 9 × 12° = 108°

∠D = 13x = 13 × 12° = 156°

Verification :

We know that,

Sum of all angles of quadrilateral = 360°

So,

∠A + ∠B + ∠C + ∠D = 360°

Substituting the values, we get,

36° + 60° + 108° + 156° = 360°

360° = 360°

L. H. S = R. H. S

Hence, it is verified.