MP Board · Class 9 · Mathematics · TrianglesIf $\triangle ABC \cong \triangle PQR$, $\angle A = 50^\circ$, and $\angle B = 60^\circ$, then what is the measure of $\angle R$?
Step-by-Step Solution
First, find $\angle C$ in $\triangle ABC$: $$\angle C = 180^\circ - (\angle A + \angle B)$$ $$\angle C = 180^\circ - (50^\circ + 60^\circ) = 180^\circ - 110^\circ = 70^\circ$$ \nSince $\triangle ABC \cong \triangle PQR$, by CPCT (Corresponding Parts of Congruent Triangles): $$\angle R = \angle C = 70^\circ$$
Detailed Options Breakdown
Option : $50^\circ$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Triangles.
Option 1: $60^\circ$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Triangles.
Option 2: $70^\circ$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: $80^\circ$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Triangles.
💡 Study Guide: This question tests core syllabus concepts from Triangles. For formulas, key summaries, and mock exam reference guides, read the full Triangles Revision Notes.