Question

angle of quadrilateral are in A.P and the greatest angle is 120

Answer 1

Let the terms of the angles be ( a - 3d ) ( a - d ) ( a + d ) ( a + 3d )

Greatest Angle = ( a + 3d ) = 120°

Sum of all angles in a quadrilateral is 360°

=> ( a - 3d ) + ( a - d ) + ( a + d ) + ( a + 3d ) = 360

=> a - 3d + a - d + a + d + a + 3d = 360

=> 4a = 360

=> a = 360 / 4 = 90°

We know that a + 3d = 120°

=> 90 + 3d = 120

=> 3d = 120 - 90

=> 3d = 30

=> d = 30 / 3 = 10°

So all the other angles are :

a - 3d = 90 - 3 * 10 => 90 - 30 = 60°

a - d = 90 - 10 = 80°

a + d = 90 + 10 = 100°

a + 3d = 120°

Hence the angles are 60°, 80°, 100° and 120°.