Question

Assertion: If the side BC of ∆ABC is produced to D, then ∠ACD = ∠A + ∠B.
Reason: The sum of the angles of a triangle is 180°.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.










Assertion:
$$\begin{gathered} \angle A+\angle B+\angle C=180°...\left(i\right)\left[\text{Sum of the angles of a triangle}\right] \\ \angle ACB+\angle ACD=180°...\left(ii\right) \end{gathered}$$
$$\begin{gathered} \mathrm{From}\left(i\right)\mathrm{and}\left(ii\right),\mathrm{we}\mathrm{get}: \\ \angle A+\angle B+\angle C=\angle ACB+\angle ACD \\ \Rightarrow \angle A+\angle B+\angle C=\angle C+\angle ACD \\ \Rightarrow \angle A+\angle B=\angle ACD \end{gathered}$$

Hence, the Assertion is true.

Reason:
Clearly, the given statement is true.
Hence, both the Assertion and Reason are true but Reason is not a correct explanation of Assertion.