In a triangle ABC, if 3∠A = 4∠B = 6∠C, calculate the angles.

The sum of the angles of a triangle is always 180°.

Answer: The angles A, B and C are 80°, 60°, and 40° respectively.

Let's calculate the angles.

Explanation:

Given: In ΔABC, 3∠A = 4∠B= 6∠C

Let us consider,

3∠A = 4∠B = 6∠C = x

Let, x = 3∠A

∠A = x/3………………….(1)

Now, x = 4∠B

∠B = x/4…………………(2)

Then, x = 6∠C

∠C = x/6…………………(3)

By using angle sum property of a triangle,

∠A + ∠B + ∠C = 180°

By substituting the values of ∠A, ∠B, ∠C from equation (1), (2) and (3)

x/3 + x/4 + x/6 = 180

By taking the LCM of the denominators 3,4 and 6 we get,

(4x + 3x + 2x)/12 = 180

9x /12 = 180

9x = 180 × 12

x = 2160/9

x = 240

Substitute the value of x in eqaution (1), (2) and (3)

∠A = x/3 = 240/3 = 80°

∠B = x/4 = 240/4 = 60°

∠C = x/6 = 240/6 = 40°

Thus, in triangle ABC, the angles are, ∠A = 80°, ∠B = 60°, ∠C = 40°.