Question

In Angle ABC, angle A : angle B : angle C = 4:5:6. Calculate Angle A, Angle B, and Angle C​

Answer 1

Answer:

Given parameters

In ΔABC,

3∠A = 4∠B= 6∠C

Let us consider x = 3∠A = 4∠B = 6∠C

x = 3∠A

∠A = x/3………………….(1)

x = 4∠B

∠B = x/4…………………..(2)

x = 6∠C

∠C = x/6…………………….(3)

By using angle sum property

∠A + ∠B + ∠C = 1800

Put the values of ∠A, ∠B, ∠C

x/3 + x/4 + x/6 = 1800

Let us find the L.C.M of 3,4,6 i.e 12

(4x + 3x + 2x)/12 = 1800

9x = 2160

x = 2400

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

∠A= x/3

∠A= 240/3 = 80°

∠B= x/4

∠B= 240/4= 60°

∠C= x/6

∠C= 240/6 = 40°

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Answer 2

Answer:

angle A=48 angle B=60 and angle C=72

Step-by-step explanation:

In Angle ABC,

the ratio angle A, angle B and angle C are 4:5:6

Let all angles are be x therefore, the sum of all angles of triangle are 180°

4x+5x+6x=180

15x=180

x=12°

therefore, angle A=4x=4×12=48°

angle B=5x=5×12=60°

angle C=6x=6×12=72°