Question

If the angles in a triangle are in the ratio 1 : 1 : 2, what kind of a triangle is it?

• A. Equilateral triangle
• B. Right angled isosceles triangle
• C. Obtuse angled triangle
• D. Scalene triangle

Answer 1

The correct option is B Right angled isosceles triangle

From Legendre's theorem, we know
"The sum of angles of any triangle is always constant and is equal to two right angles."
Let the angles be x, x and 2x.
$\therefore$ x + x + 2x = 180${}^{\circ }$
$\Rightarrow$ 4x = 180${}^{\circ }$
$\Rightarrow$ x = 45${}^{\circ }$.
The angles of the triangle are 45${}^{\circ }$, 45${}^{\circ }$ and 90${}^{\circ }$.
The triangle is therefore a right angled isosceles triangle.
$\because$ One angle is a right angle and the other two angles are equal.