Assertion (A): Using the information in the given figure, we get BC > AB > AC.

Reason (R): In △ABC,

∠BAC > ∠ACB > ∠ABC
⇒ BC > AB > AC

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.

Both A and R are true.

Explanation

According to the rule that the sum of the angles in a linear pair is 180°:

∠ BAC + 105° = 180°

⇒ ∠ BAC = 180° - 105°

⇒ ∠ BAC = 75°

∠ ABC + 135° = 180°

⇒ ∠ ABC = 180° - 135°

⇒ ∠ ABC = 45°

∠ ACB + 120° = 180°

⇒ ∠ ACB = 180° - 120°

⇒ ∠ ACB = 60°

⇒ 75° > 60° > 45°

∠BAC > ∠ACB > ∠ABC

⇒ BC > AB > AC (side opposite to greater angle is greater)

∴ Assertion (A) is true.

From the above calculations,

∠BAC > ∠ACB > ∠ABC

⇒ BC > AB > AC

∴ Reason (R) is true.

Hence, both Assertion (A) and Reason (R) are true.