Question

The measures of three angles of a triangle are in the ratio 1 : 2 : 3. Then, the triangle is a __________ triangle.

Answer 1

Let the measure of three angles of the triangle be x, 2x and 3x.

Now,

$x+2x+3x=180°$ (Angle sum property of triangle)

$\Rightarrow 6x=180°$

$\Rightarrow x=\frac{180°}{6}=30°$

$\therefore 2x=2\times 30°=60°$ and $3x=3\times 30°=90°$

So, the measure of the angles of the triangle are 30º, 60º and 90º.

Now, a triangle with one angle a right angle is called a right triangle. Thus, the triangle is a right triangle.

The measures of three angles of a triangle are in the ratio 1 : 2 : 3. Then, the triangle is a ___right___ triangle.