Question

Triangle ABC has base angles ${30}^{\circ }$ and ${120}^{\circ }$ respectively. The perimeter is $4+2\sqrt{3}$. What type of triangle is this?

• A. Right triangle
• B. Isosceles triangle
• C. Scalene triangle
• D. Equilateral triangle

Answer 1

The correct option is B Isosceles triangle

It is given that 2 of the angles are ${120}^{\circ }$ and ${30}^{\circ }$respectively.
Since the sum of the angles of a triangle is ${180}^{\circ }$, the 3^rd angle is calculated to be ${30}^{\circ }$.
As two angles of the triangle are equal, the triangle is isosceles.