One of the angles of a quadrilateral is thrice the smaller angle of a parallelogram. The respective ratio between the adjacent angles of the parallelogram is ` 4 : 5` Remaining three angles of the quadrilateral are in ratio ` 4 : 11 : 9` respectively.What is the sum of the largest and the smallest angles of the quadrilateral?

Options

A. `255^(@)`
B. ` 260^(@)`
C. ` 265^(@)`
D. ` 270^(@)`

Answer

B

Explanation

Let the adjacent of the parallelogram be 4x and 5x.
`:. 4x+5x= 180 or 9x = 180 :. X = 20`
One angle of quadrilateral `= 3 xx 80^(@) = 240^(@)`
Again, sum of angles of quadrilateral
` 4y+11y+ 9y+ 240^(@) = 360^(@)`
` 24y= 120^(@) :. y = 5`
Hence, the sum of the largest and the smallest angles of the quadrilateral = ` 4 xx 5 + 240 = 260^(@)`