Question
Download Solution PDFThe angles of a quadrilateral are in the ratio 2 ∶ 5 ∶ 7 ∶ 10. Find the difference between the greatest and the smallest angles of the quadrilateral.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Ratio of angles of quadrilateral = 2 ∶ 5 ∶ 7 ∶ 10
Concept:
Since, we know that the sum of angles of a quadrilateral is 360°, using this property calculate the values of all the angles of the quadrilateral.
Calculation:
Let, the angles be 2x, 5x, 7x, 10x.
2x + 5x + 7x + 10x = 360°
⇒ 24x = 360°
⇒ x =\(360^\circ\over 24\)
⇒ x = 15°
Largest angle = 10x = 10 × 15° = 150°
Smallest angle = 2x =2 × 15° = 30°
Difference between the smallest and the largest angle = 150° - 30° = 120°
∴ '120°' is the difference between the largest and the smallest angle.
Last updated on Jul 11, 2025
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