Question : If one angle of a triangle is equal to half the sum of the other two equal angles, then the triangle is:
Option 1: isosceles
Option 2: scalene
Option 3: equilateral
Option 4: right-angled
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Correct Answer: equilateral
Solution : Let the two equal angles as $\alpha$ and the third angle as $\beta$. According to the problem, $\beta$ is equal to half the sum of the other two angles. $⇒\beta = \frac{1}{2}(2\alpha) = \alpha$ Hence, the angles are $\alpha, \alpha$, and $\alpha$. So, each angle in the triangle is equal, Therefore, this is an equilateral triangle. Hence, the correct answer is 'equilateral'.
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