In an isosceles triangle $ABC$ with $AB = AC$, if $\angle B = 50^\circ$, then what is the measure of $\angle A$?

Q: In an isosceles triangle $ABC$ with $AB = AC$, if $\angle B = 50^\circ$, then what is the measure of $\angle A$?

In $\triangle ABC$, since $AB = AC$, the angles opposite to these equal sides are also equal: $$\angle C = \angle B = 50^\circ$$ \nAccording to the Angle Sum Property of a triangle: $$\angle A + \angle B + \angle C = 180^\circ$$ $$\angle A + 50^\circ + 50^\circ = 180^\circ$$ $$\angle A + 100^\circ = 180^\circ$$ $$\angle A = 180^\circ - 100^\circ = 80^\circ$$ \nHence, the measure of $\angle A$ is $80^\circ$.

Question

Accepted Answer

In $	riangle ABC$, since $AB = AC$, the angles opposite to these equal sides are also equal: $$\angle C = \angle B = 50^\circ$$ 
According to the Angle Sum Property of a triangle: $$\angle A + \angle B + \angle C = 180^\circ$$ $$\angle A + 50^\circ + 50^\circ = 180^\circ$$ $$\angle A + 100^\circ = 180^\circ$$ $$\angle A = 180^\circ - 100^\circ = 80^\circ$$ 
Hence, the measure of $\angle A$ is $80^\circ$.

MP Board · Class 9 · Mathematics · TrianglesIn an isosceles triangle $ABC$ with $AB = AC$, if $\angle B = 50^\circ$, then what is the measure of $\angle A$?