Question

The angles of a quadilateral are in AP whose common difference is 10 degree. Find the angels

Answer 1

Since the angles are in A.P., let the angles are p, p+10, p+20, p+30
sum of angles=360
⇒ p + p+10 + p+20 + p+30 = 360
⇒ 4p + 60 = 360
⇒ 4p = 360-60 = 300
⇒ p = 300/4 = 75

So the angles are
p = 75
p+10 = 75+10 = 85
p+20 = 75+20 = 95
p+30 = 75+30 = 105

Answer 2

We know the sum of angles of Quadrilateral =360 degree
Let smallest angle be = Ф
As the angles are in AP we have angles Ф, Ф+10,Ф+20,Ф+30
Then we have  Ф+Ф+10+Ф+20+Ф+30 = 360
                     ⇒ 4Ф + 60 = 360
                     ⇒ 4Ф = 360
                     ⇒ Ф = 300/4 = 75
Hence  the angles  of quadrilateral  are 75, 75+10 ,75+20,75+30
                                                   or 75,85,95,105