#### Question 4:

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:

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

A.T.Q,

∠Q = 2∠P

∠R = 2∠P

Now, ∠P + ∠Q + ∠R = 180∘ (Angle sum property)

⇒ ∠P + 2∠P + 3∠P = 180∘

⇒ 6∠P = 180∘

⇒ ∠P

Therefore,

∠P = 30∘

∠R = 60∘

∠R = 90∘

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

A.T.Q,

∠Q = 2∠P

∠R = 2∠P

Now, ∠P + ∠Q + ∠R = 180∘ (Angle sum property)

⇒ ∠P + 2∠P + 3∠P = 180∘

⇒ 6∠P = 180∘

⇒ ∠P

*= 30∘*Therefore,

∠P = 30∘

∠R = 60∘

∠R = 90∘

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