Question

the angles of a cyclic quadrilateral are consecutive terms of arithmetic sequence and one of the angles is 45°.what is the measure of the angle opposite to 45° angle?

Answer 1

Opposite angles add up to 180º

Opposite angle = 180 - 45 = 135º

Let the difference be d.

First angle = 45º (Given)  

Second angle = 45 + d

Third angle = 45 + 2d = 135

Fourth angle = 45 + 3d

45 + (45 + d) + 135 + (45 + 3d) = 360

45 + 45 + d + 135 + 45 + 3d = 360

4d + 370 = 360

4d = 90

d = 22.5

Second angle = 45 + d = 45 + 22.5 = 67.5º

Fourth angle = 45 + 3d = 45 + 3(22.5) = 112.5º

The opposite angle is 135º and the 2 other angles are 67.5º and 112.5º