In the diagram, PQRS is a circle. find the value of x.
-
50°
- 30°
- 80°
- 100°
The correct answer is: A
Explanation
Opp. angles in a cyclic quadrilateral always add up to 180°
∠P + ∠R & ∠Q + ∠S = 180
x + x+y = 180
2x + y = 180... i
2y - 30 + x = 180
2y + x = 180 + 30
x + 2y = 210 ... ii
Elimination method:
(2x + y = 180) * 1 --> 2x + y = 180
(x + 2y = 210) * 2 --> 2x + 4y = 420
Subtracting both equations
- 3y = - 240
y = 80°
using eqn i
2x + y = 180
2x + 80 = 180
2x = 100
x = 50°