The angles of a quadrilateral are in A. P. with common difference 20∘. Find its angles.
The angles of quadrilateral are in A.P. with common difference, d = 20∘
Let the first angle be 'a'
Then,
Second angle = a + d = a + 20∘
Third angle = a + 2d = a + 40∘
Fourth angle = a + 3d = a + 60∘
We know that the sum of all angles of a quadrilateral is 360∘
⇒ a + a+20∘ + a+40∘ + a+60∘ = 360∘
⇒ 4a + 120∘ = 360∘
⇒ 4a = 360∘ - 120∘
⇒ 4a = 240∘
⇒ a = 240∘4
⇒ a = 60∘
First angle = 60∘
Second angle = 60∘ + 20∘ = 80∘
Third angle = 60∘ + 40∘ = 100∘
Fourth angle = 60∘ + 60∘ = 120∘
Hence, the angles of given quadrilateral are 60∘, 80∘, 100∘, 120∘