MP Board · Class 9 · Mathematics · TrianglesIn an isosceles triangle $ABC$ with $AB = AC$, if $\angle A = 80^\circ$, then what is the measure of $\angle B$?
Step-by-Step Solution
In $\triangle ABC$, $AB = AC$, which means angles opposite to equal sides are equal.\nHence, $\angle B = \angle C$. \nSum of angles in a triangle = $180^\circ$ $$\angle A + \angle B + \angle C = 180^\circ$$ $$80^\circ + \angle B + \angle B = 180^\circ$$ $$2\angle B = 180^\circ - 80^\circ = 100^\circ$$ $$\angle B = 50^\circ$$
Detailed Options Breakdown
Option : $50^\circ$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: $80^\circ$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Triangles.
Option 2: $100^\circ$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Triangles.
Option 3: $40^\circ$
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.