Question

The angles of a quadrilateral are in the ratio 2:3:6:7. Find the largest angle of the Quadrilateral.

Answer 1

The angles of a quadrilateral are given as in the ratio 2:3:6:7
Let the angles be 2x, 3x, 6x, 7x.
The sum of angles of a quadrilateral = 360°
⇒2x+3x+6x+7x = 360
⇒18x = 360
⇒x = 360/18
∴x = 20
∴The largest angle = 7x = 7×20 =140° 

Answer 2

The largest angle of the Quadrilateral is 140° if angles of a quadrilateral are in the ratio 2:3:6:7

Given:

• Angles of a quadrilateral are in the ratio 2:3:6:7

To Find:

• The largest angle of the Quadrilateral.

Solution:

• Sum of all the angles of a quadrilateral is 360°

Step 1:

Assume that angles are:

2x, 3x ,6x and 7x  

Step 2:

Add all the angles and equate with 360°

2x + 3x + 6x + 7x = 360°

Step 3:

Solve for x:

18x = 360°

=> x = 20°

Step 4 :

Substitute x = 20° in each angle

2x = 2 * 20° = 40°

3x = 3 * 20° = 60°

6x = 6 * 20° = 120°

7x = 7 * 20° = 140°

Step 5 :

Identify the largest angle

140°

The largest angle of the Quadrilateral is 140°