Question

If two angles of a triangle are ${60}^{\circ }$ each, then the triangle is a / an ______ triangle.

• A. Isosceles but not equilateral
• B. scalene
• C. equilateral
• D. right-angled

Answer 1

The correct option is C equilateral

In $\Delta ABC$,
$\angle A+\angle B+\angle C={180}^{\circ }$ [angle sum property of a triangle]
$\Rightarrow \angle A+{60}^{\circ }+{60}^{\circ }={180}^{\circ }$ $[\because \angle B=\angle C={60}^{\circ }$, given]
$\Rightarrow \angle A+{120}^{\circ }={180}^{\circ }$
$\Rightarrow \angle A={60}^{\circ }$

Since, all the angles are of ${60}^{\circ }$. So, it is an equilateral triangle.
Hence, option (c) is correct.