Question

the angles of a quadrilateral are in ap whose common difference is 10degree find the angles

Answer 1

Let the first angle be a

Second angle = a + 10

Third angle = a + 20

Fourth angle = a + 30

By angle sum property of quadrilateral,

a + a + 10 + a +20 + a + 30 = 360

=> 4a + 60 = 360

=> 4a = 300

=> a = 75

First angle = 75°

Second angle = 85°

Third angle = 95°

Fourth angle = 105°

Answer 2

Sum of all angles in a quadrilateral is 360, there are four angles in a quadrilateral.
An AP is in the form :a, a+d, a+2d,a+3d.. There fore a+a+d+a+2d+a+3d=360, 4a+6d=360.
2a+3d=180. 10is the d. Therefore, 2a+3*10=180 here * means multiplication. 2a+30=180, 2a=150,a=75.applying a and d in the AP:75,75+10,75+2*10,75+3*10 . There fore the angles are 75,85,95,105