The angles of a cyclic quadrilateral, taken in order are x°, (3x - 30)°, (y + 30)° and (2x - y)°. Find the measure of the smallest angle of the quadrilateral.

30°

The angles of a cyclic quadrilateral, taken in order are x°, (3x - 30)°, (y + 30)° and (2x - y)°

We know that,

The sum of opposite angles of a cyclic quadrilateral is = 180°

So,  x° + (y + 30)° = 180° ----(1)

and (3x - 30)° + (2x - y)° = 180°----(2)

x + y = 150

amd 5x - y = 210

Add both equation,

x + y + 5x - y = 360

6x = 360

x = 60^o

Put x in either 1 or 2

x° + (y + 30)° = 180°

= 60° + (y + 30)° = 180°

= y = 90°

Calculate the four angles of the quadrilateral:

x  =60°

3x−30 = 3(60)−30 = 180−30=150°

y+30 = 90+30 = 120°

2x−y = 2(60)−90 = 120−90=30°