Question

the angle of quadrilateral are inthe ratio 3:5:9:13 find all the angles of the quadrilateral​

Answer 1

Given:

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

To Find:

• All angles of quadrilateral.

Solution:

Let angles in the ratio 3 : 5 : 9 : 13 be a, b, c, & d, where x is any number.

Let,

• a = 3x
• b = 5x
• c = 9x
• d = 13x

As we know:

Sum of angles of quadrilateral is 360°.

According to the question:

→ a + b + c + d = 360° [Angle sum property of quadrilateral]

→ 3x + 5x + 9x + 13x = 360°

→ 30x = 360°

→ x = 360°/30

→ x = 12°

Therefore,

The angles are

• a = 3x = 3 × 12 = 36°
• b = 5x = 5 × 12 = 60°
• c = 9x = 9 × 12 = 108°
• d = 13x = 13 × 12 = 156°

Hence,

• All angles of quadrilateral are 36°, 60°, 108° and 156°.