Gnpth wrote:
The exterior angles of a quadrilateral are in the ratio 1:4:4:6. What is the difference between the largest and the smallest interior angles of the quadrilateral?
(A) 110
(B) 60
(C) 140
(D) 120
(E) 100
Sum of all exterior angles is 360 so we can just use fractions for largest and smallest proportions to find their corresponding angle in degrees.
Sum of proportions = \(1 + 4 + 4 + 6 = 15\)
Smallest exterior angle:
\(1/15 * 360 = 24\)
Largest exterior angle:
\(6/15 * 360 = 144\)
interior angle + exterior angle = 180.
interior angle = 180 - exterior angle.
Naturally largest interior angle will be corresponding to the smallest exterior angle and smallest interior angle will be angle corresponding to the largest exterior angle.
Largest interior angle = 180 - smallest exterior angle = \(180 - 24 = 156\)
Smallest interior Angle = 180 - largest exterior angle = \(180 - 144 = 36\)
Difference = \(156 - 36 = 120\)
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