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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