Question

If angles of a triangle are in the ratio 1:2:3. Find the value of each angle.

Answer 1

Hint: Take the ratio of the interior angles as the proportionality. Use the angle sum property of triangle i.e. the sum of all the interior angles of a triangle is equal to $ 180^\circ $ .

Complete step-by-step answer:

Let's say the common ratio of angles of the triangle is $ x $ .
Sum of all the interior angles of a triangle is $ 180^\circ $ ..
So, all three interior angles of a triangle are $ x $ , $ 2x $ and $ 3x $ respectively.
Sum of all three interior angles of a triangle is $ 180^\circ $ ..
 $
  x + 2x + 3x = {180^.} \\
   \Rightarrow 6x = 180^\circ \\
   \Rightarrow x = \dfrac{{180^\circ }}{6} = 30^\circ \\
  $
So, the measure of the first angle of the triangle is equal to $ 30^\circ $ .
The measure of the second angle of the triangle is equal to $ 2 \times 30^\circ = 60^\circ $ .
The measure of the third angle of the triangle is equal to $ 3 \times 30^\circ = 90^\circ $ .
All angles are acute angles in a triangle.

<Note: Remind that an angle is acute if its measure is less than $ 90^\circ $, is right angle if the measure is equal to $ 90^\circ $ and is obtuse if its measure is greater than $ 90^\circ $ . The triangle with a right angle is known as right angled triangle.