Question

The angles of a triangle are in the ratio $1:2:3$. What are the measures of the angles of the triangle? What special name can you give to this triangle?

Answer 1

Step I - Let the angle be $\text{x}$.

So the angles are $\text{x, 2x, 3x}$.

Step II - As we know that sum of the angles of the triangle is $180°$.

So, $\text{x + 2x + 3x = 180°}$

$\text{6x = 180°}$

$\text{x = 180° ÷ 6}$

$\text{x = 30°}$

Hence the angles of the triangle are $30°,2\times 30°=60°,3\times 30°=90°$.

Since, one of the given angles is equal to $90°$, therefore It is a right-angled triangle.