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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