Question

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

Answer 1

Acc. to it
the angles must be
40, 60 ,100 160
so supplementary of 160 is 20
and, complement of 40is 50
so the ans. is 20+50= 70

Answer 2

The sum of supplement of the largest angle and the complement of the smallest angle is 70°.

• The angles of the quadrilateral are in the ratio 2:3:5:8.

• Let the common ratio be x.

• Therefore, the angles of the quadrilateral are 2x,3x,5x and 8x.

• The sum of all angels of the quadrilateral is 360°.

2x+3x+5x+8x = 360°

18x = 360°

x = 20°

• Now the angles of the quadrilateral are 40°,60°,100° and 160°.
• Smallest angle is 40° and largest angle is 160°.

• Now the supplement of largest angle is 180° - 160° = 20°

• Complement of the smallest angle is 90°-40° = 50°

• Sum of complement of smallest angle and the supplement of the largest angle = 50°+20° = 70°