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If the angles of a quadrilateral are in the ratio of 4: 9: 11: 12, then the largest of these angles is:
Question

If the angles of a quadrilateral are in the ratio of 4: 9: 11: 12, then the largest of these angles is:

A.

72°

B.

120°

C.

168°

D.

166°

Correct option is B

Given:
Angles of a quadrilateral are in the ratio of 4: 9: 11: 12
Solution:
Angles of the quadrilateral be 4x, 9x, 11x, and 12x
The sum of the angles of a quadrilateral is 360°
4x + 9x + 11x + 12x = 360°
36x = 360°
x = 10°
The angles of the quadrilateral are
4x = 40°, 9x = 90°, 11x = 110°and 12x = 120°
The largest angle is 12x = 12×\times​10° = 120°.
Therefore, the largest angle is 120°.

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