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Q39

0. The angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8. The sum of the supplement of the largest angle and the complement of the smallest angle is

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Option : D
Explanation : Let 2x, 3x, 5x and 8x be the angles of the quadrilateral.
Sum of angles of a quadrilateral = 360 °
⇒ 2x+3x+5x+8x=360^o
⇒ 18x=360° ⇒ x=20° Now, smallest angle = 2x = 2 x 20° = 40^o
Complement of the smallest angle = 90^o- 40° = 50°...(i)
Largest angle=8x =8 x20^o =160°
Supplement of the largest angle= 180° -160° = 20° ... (ii)
Now, sum of the supplement of largest
angle and complement of smallest angle= 20^o +50°= 70^o

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