Question

The measure of one of the angles of a triangle is twice the measure of its smallest angle and the measure of the other is thrice the measure of the smallest angle. Find the measures of the three angles.

Answer 1

Let us suppose the angles of a ΔPQR such that ∠P < ∠Q < ∠R.

∴ ∠Q = 2∠P

∴ ∠R = 3∠P

Now, ∠P + ∠Q + ∠R = 180°      ...(The sum of the angles of a triangle is 180°.)

⇒ ∠P + 2∠P + 3∠P = 180°         

⇒ 6∠P = 180°  

∠P = `(180°)/6`

∴ ∠P = 30°

∠Q = 2∠P = 2 × 30° = 60°

∠R = 3∠P = 3 × 30° = 90°

Hence, the measure of each angle is 30°, 60° and 90° respectively.