Question

If the angles of a four sided polygon are in the ratio 7:8:9:12, then the angles would be?

(a) 70, 80, 90, 100

(b) 70, 70, 80, 80

(c) 120, 70, 80, 100

(d) 70, 80, 90, 120

This question was posed to me in an internship interview.

Origin of the question is Quadrilaterals in chapter Quadrilaterals of Mathematics – Class 8

Answer 1

Right choice is (d) 70, 80, 90, 120

The best I can explain: Let us assume x to be the common multiple.

Now, the sides of the four sided polygon would be 7x, 8x, 9x and 12x.

The sum total of any four sided polygon is 360°.

Therefore 7x+8x+9x+12x=360

Therefore 36x=360

Therefore x=10°

Therefore the angles are, 7x=70, 8x=80, 9x=90 and 12x=120.

One can recheck their answer by, verifying the total as One can recheck their answer by, verifying the total as 360°.