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.
Answer & explanation
Correct answer: option 2
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°