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

Given: 3∠P = 4∠Q = 6∠R

Formula Used/Theory:-

→ Angle sum property

Sum of all angles of triangle is 180°

Solutions:-

If 3∠P = 4∠Q = 6∠R

Taking LCM of 3,4,6

We get 12

Then;

Dividing LCM by magnitude of each angle gives ratio of all 3 angles

∠P = 12/3 = 4

∠Q = 12/4 = 3

∠R = 12/6 = 2

Means angles are in ratio 4:3:2

Then;

Let all 3 angles of triangle be 4x;3x;2x

By angle sum property

4x + 3x + 2x = 180°

9x = 180°

x = = 20°

The angles of triangle will be 4×20°;3×20°;2×20°

The angles of triangle are 80°;60°;40°

Result:- The angles of triangle are 80°;60°;40°