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. |
20° 30° 40° 50° |
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 = 60o 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° |