In the diagram, PQRS is a circle. find the value of x.

  • A 50°
  • B 30°
  • C 80°
  • D 100°
waec 2021mathematics

The correct answer is A. 50°

Opp. angles in a cyclic quadrilateral always add up to 180°

∠P + âˆ R & âˆ Q + âˆ 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°

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