In the figure shown above, quadrilateral PQRS has its vertices on the circumference of the circle with centre O. If ∠QOS = 20x° and ∠QRS = 26x°, then what is the value of ‘x’?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 5.
The angle at the center of a circle is twice the angle at the circumference.
So, ∠SPQ = (1/2)∠QOS
⇒ ∠SPQ = (1/2) × 20x° = 10x°
In a cyclic quadrilateral, the sum of any pair of opposite angles is 180°.
So, ∠QRS + ∠SPQ = 180°
⇒ 26x° + 10x° = 180°
⇒ 36x° = 180°
⇒ x = 180°/36° = 5