Question

Find the angles of a quadrilateral which is in AP with common difference 20.

Answer 1

Heya user !!!

Here's the answer you are looking for

Let one angle be a, since the angles are in AP and the common difference is 20, the other angles are (a + 20), (a + 40), (a + 60).


Also, the sum of all the interior angles of a quadrilateral is 360°.

So, a + (a + 20) + (a + 40) + (a + 60) = 360

4a + 120 = 360

4a = 360 - 120 = 240

a = 240/4 = 60

So, the other angles are (60 + 20) = 80, (60 + 40) = 100 and (60 + 60) = 120

Therefore, the interior angles are 60°, 80°, 100°, 120°.



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Answer 2

let angles are x,x+d,x+2d,x+3d ,where d is Common difference.
now as sum of angles of a quadrilateral is 360°
x+x+d+x+2d+x+3d=360
4x+6d =360
4x +6×20=360
4x =360-120
4x=240
x=60°
angles are 60,60+20,60+2×20,60+3×20
I.e. 60°,80°,100°,120°