Question

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

Answer 1

Answer:

27, 45, 81, 117

Step-by-step explanation:

well.. here you go

1. ratio of angles is 3:5:9:13

2. 1st angle= (3/40)*360 =27 deg

3. 2nd angle=(5/40)*360 =45 deg

4. 3rd angle=(9/40)*360 =81 deg

5. 4th angle=(13/40)*360 =117 deg

done. as simple as that

Answer 2

$\bigstar$ Given:

• Ratio of the angles of a quadrilateral = $3:5:9:13$

$\bigstar$ To Find:

• All the angles of the quadrilateral.

$\bigstar$ Solution:

Let us consider the common ratio between the angles as x

We know that,

The sum of the interior angles of the quadrilateral = $360^{o}$

Now,

$3x + 5x + 9x + 13x = 360^{o}\\\implies 30x = 360^{o}$

Finding the value of x

$\implies x = \frac{360}{30} \\\implies x = 12^{o}$

Therefore, angles of the quadrilateral are:

$3x = 3 \times 12^{o} = \boxed{\underline{\underline{36^{o}}}}$

$5x = 5 \times 12^{o} = \boxed{\underline{\underline{60^{o}}}}$

$9x = 9 \times 12^{o} = \boxed{\underline{\underline{108^{o}}}}$

$13x = 13 \times 12^{o} = \boxed{\underline{\underline{156^{o}}}}$