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The angles of a quadrilateral are in the ratio 4 : 7 : 6 : 13. What is the difference between the smallest and the greatest angles of the quadrilateral?

The angles of a quadrilateral are in the ratio 4 : 7 : 6 : 13. What is the difference between the smallest and the greatest angles of the quadrilateral? Correct Answer 108° 

Given:

Ratio of angles of quadrilateral = 4 : 7 : 6 : 13

Concept:

Sum of all the angles in quadrilateral is 360°

Calculation:

Let the angles of the quadrilateral be 4x, 7x, 6x, and 13x

⇒ 4x + 7x + 6x + 13x = 360°

⇒ 30x = 360°

⇒ x = 12°

Greatest angle = 13 × 12 = 156° 

Smallest angle = 4 × 12 = 48° 

Difference between the greatest and the smallest angle = 156° - 48°  

⇒ 108°  

∴ The difference between the greatest and the smallest angle is 108° 

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