Question

All 4 angles of a quadrilateral are in AP.if the sum of first 3 angles is twice of fourth then find all angles

Answer 1

Hello friend,
Let 1st angle be a.
2nd angle=a+d
3rd angle=a+2d
4th angle=a+3d
Given:-
a+a+d+a+2d=2(a+3d)
3a+3d=2a+6d
3a-2a=6d-3d
a=3d
a+a+d+a+2d+a+3d=360°
4a+6d=360
4(3d)+6d=360
18d=360
d=20°
a=3×20=60°
so angles are 60°,80°,100° and 120°.
hope it helps.

Answer 2

let the angles be a, a+d, a+2d and a+3d
ATQ,
a+a+d+a+2d=2(a+3d)
3a+3d=2a+6d
3a-2a+3d-6d=0
a-3d=0
a=3d
Also,
a+a+d+a+2d+a+3d=360
4a+6d=360
2a+3d=180
2(3d)+3d=180
6d+3d=180
9d=180
d=20
So,
a=3d
a=3×20
a=60
So the angles are 60, 80, 100 and 120