Assertion (A): In the figure, if O is the centre of the circle, then ∠BCD = 80°.

Reason (R): Exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

From figure,

The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

Reflex AOB = 360° - 100° = 260°

∠ACB = $\dfrac{1}{2}$ Reflex ∠AOB

∠ACB = $\dfrac{260 ^{\circ}}{2}$

∠ACB = 130°

∠ACB + ∠BCD = 180° [Linear pair]

∠BCD = 180° - 130°

∠BCD = 50°

So assertion (A) is false.

We know that,

In, cyclic quadrilaterals if one side is extended, the exterior angle formed is equal to the interior opposite angle.

So, reason (R) is true.

A is false, R is true

Hence, option 2 is the correct option.