The angles of a quadrilateral are in A.P. and the greatest angle is
120∘. Express the angles in radians.
Let the angles in degrees be a - 3d, a - d, a + d, a + 3d
Then,
Sum of the angles =360∘
⇒ 4a=360∘a=90∘
Also,
greatest angle =120∘
a + 3d = 120∘
⇒ 90∘+3d=120∘⇒ 3d=30∘
⇒ d=10∘
Hence, angles in degrees
60∘, 80∘, 100∘, 120∘
and in radians, we know that
1∘=(π180)c∴ 60×π180=π3, 80×π180=4π9,100×π180=5π9 and 120×π180=2π3∴ π3, 4π9, 5π9, 2π3