Question

In ΔPQR, if 3∠P = 4∠Q = 6∠R, calculate the angles of the triangle.

Answer 1

Given, 3∠P = 4∠Q = 6∠R

Then, ∠P = `6/3`∠R = 2∠R

∠Q = `6/4`∠R = `3/2`∠R

In ΔPQR,

∠P + ∠Q + ∠R = 180°  ...[Angle sum property of a triangle]

⇒ 2∠R + `3/2`∠R + ∠R = 180°

⇒ 3∠R + `3/2`∠R = 180°

⇒ 6∠R + 3∠R = 180° × 2  ...[On taking LCM in LHS]

⇒ 9∠R = 360°

⇒ ∠R = `360^circ/9` = 40°

∴ ∠P = 2∠R = 2 × 40° = 80°

And ∠Q = `3/2`∠R = `3/2` × 40° = 60°

Hence, all the angles of the triangle are 80°, 60° and 40°.