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Q.
The angles of a quadrilateral are in the ratio of 2:4:7:5. The smallest angle of the quadrilateral is equal to the smallest angle of a triangle. One of the angles of the triangle is twice the smallest angle of the triangle. What is the second largest angle of the triangle ?
A.
80 degrees
B.
60 degrees
C.
120 degrees
D.
40 degrees
View Answer
Correct choice: B
Explanation:
Given the angles of a quadrilateral are in the ratio of 2:4:7:5 Let the angles of a quadrilateral are 2x, 4x, 7x, 5x But we know that sum of the angles = 360 degrees. => 2x + 4x + 7x + 5x = 360 => x = 20 Therfore, the smallest angle of the quadrilateral = 2x = 2x20 = 40 degrees. One of the angle of the triangle = 2 x 40 = 80 degrees The other angle is 180 - (40 + 80) = 60 degrees. Hence the second largest angle of the triangle is 60 degrees.
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