Question

If the angle of a triangle is in ratio 1:2:3, find the measure of the smallest angle.

Answer 1

Let us consider the angles of the triangle are $x,2x,\mathrm{and}3x$

We know that the sum of all interior angles of a triangle is 180°,

Finding the value of x:

From the angle sum property of a triangle we can write;

$$\begin{gathered} x°+2x°+3x°=180° \\ 6x°=180° \\ x°=30°. \end{gathered}$$

Therefore, the three angles of a triangle will be 30°, 60°, and 90°.

Hence, the measure of the smallest angle is 30°.