Of the three angles of a triangle, one is twice the smallest and mother one is thrice the smallest. Find the angle.

Question

Philoid · Accepted Answer

60°, 90°, 30°

Let ∠P, ∠Q and ∠R are three angles of triangle PQR,

And ∠P is the smallest angle.

Now,

∠Q = 2 ∠P ________________ (i)

∠R = 3 ∠P ________________ (ii)

We know that sum of angles of triangle = 180°

∠P + ∠Q + ∠R = 180° [Sum of angles]

⇒ ∠P + 2 ∠P + 3 ∠P = 180° [From equation (i) and (ii)]

⇒ 6 ∠P = 180°

⇒ ∠P = 30°

Therefore,

⇒ ∠Q = 2 ∠P = 60° [from equation (i)]

⇒ ∠R = 3 ∠P = 90° [from equation (ii)]