Question : In an isosceles triangle, if the unequal angle is 4 times the sum of the equal angles, then each equal angle is:
Option 1: $25^{\circ}$
Option 2: $30^{\circ}$
Option 3: $21^{\circ}$
Option 4: $18^{\circ}$
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Correct Answer: $18^{\circ}$
Solution :
In an isosceles triangle, two angles are equal. Let the equal angles be $\angle B$ and $\angle C$ ($\angle B=\angle C$). The third angle which is unequal is $\angle A$. Given that the unequal angle is $4$ times the sum of the equal angles. $=4(\angle B+\angle C)$ $=4(\angle B+\angle B)$ $=4(2\angle B)$ $=8\angle B$ The sum of the angles in a triangle is always $180^{\circ}$. $=2\angle B+ 8\angle B = 180^{\circ}$ $=10\angle B = 180^{\circ}$ $=\angle B= 18^{\circ}$ Hence, the correct answer is $18^{\circ}$.
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