Question
Download Solution PDFThe angles of a quadrilateral are in the ratio of 1 : 3 : 4 : 7. The difference between the largest and the smallest angle is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The angles of a quadrilateral are in the ratio 1 : 3 : 4 : 7.
Formula used:
Sum of angles in a quadrilateral = 360°
Let the angles be x, 3x, 4x, and 7x.
Calculation:
Sum of angles: x + 3x + 4x + 7x = 360
⇒ 15x = 360
⇒ x = 360 ÷ 15
⇒ x = 24
Angles are:
Smallest angle = x = 24°
Largest angle = 7x = 7 × 24 = 168°
Difference between the largest and smallest angle:
⇒ 168° - 24° = 144°
∴ The correct answer is option (3).
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