Question

The angles of a quadrilateral are in the ratio if 3 : 4 : 5 : 6. find all the angles​

Answer 1

Given:

A quadrilateral with

• Angles in ratio = 3 : 4 : 5 : 6

What To Find:

We have to find the angles of the quadrilateral.

How To Find:

To find the angles, we have to

• Use the property and.
• Take x as a common measure and form a linear equation.

Property For Finding:

Sum of Angles of Quadrilateral = 360°

Solution:

Using the property,

⇒ Sum of Angles of Quadrilateral = 360°

Substitute the values,

⇒ 3x + 4x + 5x + 6x = 360°

Add the like terms in LHS,

⇒ 18x = 360°

Take 18 to RHS,

⇒ $\sf x = \dfrac{360}{18}$

Divide 360 by 18,

⇒ x = 20°

Now, substitute the values,

• 1st angle = 3x = 3 × 20 = 60°
• 2nd angle = 4x = 4 × 20 = 80°
• 3rd angle = 5x = 5 × 20 = 100°
• 4th angle = 6x = 6 × 20 = 120°

∴ Therefore, the angles of a quadrilateral are 60°, 80°, 100°, and 120°.

Answer 2

Given:

A quadrilateral with

Angles in ratio = 3 : 4 : 5 : 6

What To Find:

We have to find the angles of the quadrilateral.

How To Find:

To find the angles, we have to

Use the property and.

Take x as a common measure and form a linear equation.

Property For Finding:

Sum of Angles of Quadrilateral = 360°

Solution:

Using the property,

⇒ Sum of Angles of Quadrilateral = 360°

Substitute the values,

⇒ 3x + 4x + 5x + 6x = 360°

Add the like terms in LHS,

⇒ 18x = 360°

Take 18 to RHS,

⇒ $\sf x = \dfrac{360}{18}$

Divide 360 by 18,

⇒ x = 20°

Now, substitute the values,

1st angle = 3x = 3 × 20 = 60°

2nd angle = 4x = 4 × 20 = 80°

3rd angle = 5x = 5 × 20 = 100°

4th angle = 6x = 6 × 20 = 120°

∴ Therefore, the angles of a quadrilateral are 60°, 80°, 100°, and 120°.