MCQMathematics

MP Board · Class 9 · Mathematics · TrianglesIn $\Delta ABC$, if $AB = AC$ and $\angle B = 50^\circ$, then the measure of $\angle A$ is:

Q: In $\Delta ABC$, if $AB = AC$ and $\angle B = 50^\circ$, then the measure of $\angle A$ is:

Correct Answer: $80^\circ$ Calculation:\nIn $\Delta ABC$, since $AB = AC$, the angles opposite to equal sides are equal.\nTherefore, $\angle C = \angle B = 50^\circ$. \nUsing the angle sum property of a triangle: $$\angle A + \angle B + \angle C = 180^\circ$$ $$\angle A + 50^\circ + 50^\circ = 180^\circ$$ $$\angle A + 100^\circ = 180^\circ$$ $$\angle A = 180^\circ - 100^\circ = 80^\circ$$

Step-by-Step Solution

Correct Answer: $80^\circ$

Calculation:\nIn $\Delta ABC$, since $AB = AC$, the angles opposite to equal sides are equal.\nTherefore, $\angle C = \angle B = 50^\circ$. \nUsing the angle sum property of a triangle: $$\angle A + \angle B + \angle C = 180^\circ$$ $$\angle A + 50^\circ + 50^\circ = 180^\circ$$ $$\angle A + 100^\circ = 180^\circ$$ $$\angle A = 180^\circ - 100^\circ = 80^\circ$$

Detailed Options Breakdown

Option : $50^\circ$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Triangles.

Option 1: $80^\circ$ (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

Option 2: $100^\circ$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Triangles.

Option 3: $130^\circ$

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.

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