Question

Assertion (A): If $$\triangle ABC\sim\triangle DEF$$, $$\angle A=47^{\circ}$$ and $$\angle E=83^{\circ}$$ then $$\angle C=50^{\circ}$$.

Reason (R): Similar triangles are always equiangular.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

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

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. Similarity gives $$\angle B=\angle E=83^{\circ}$$, so the angles of $$\triangle ABC$$ sum to $$180^{\circ}$$: $$\angle C=180^{\circ}-(47^{\circ}+83^{\circ})=50^{\circ}$$

Step 2 – Reason: R is true. Similar triangles have equal corresponding angles.

Step 3 – Link: Equiangularity gives $$\angle B=\angle E$$, which together with the angle sum of a triangle establishes the asserted value of $$\angle C$$.