Discussion
In a triangle ABC, ∠A = 100° and sides AB and AC are equal. Then value of ∠B is
Answer: C
Angle B is 40°.
Since AB = AC, the triangle is isosceles and the base angles B and C are equal. The angles of a triangle sum to 180°:
\[ \begin{aligned} \angle B + \angle C &= 180^{\circ} - 100^{\circ} = 80^{\circ} \\ \angle B &= \frac{80^{\circ}}{2} = 40^{\circ} \end{aligned} \]
50° comes from halving 100° instead of the remaining 80°, and 60° and 45° would not give a total of 180° with equal base angles.
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