Question

in a triangle abc if 3angle a =4angle b =6angle c calculate the angles
​

Answer 1

Step-by-step explanation:

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°

I hope it would helpful for u

Please make me as Brianlist

Answer 2

Given:-

In a triangle 3 angle A = 4 angle B = 6 angle C

To find:-

Measure of angles?

Solution:-

According to angle sum property:-

$\angle \: a + \angle \:b + \angle \: c = 180 \degree$

Let the angle be 'x'

$3 \angle \: a = 4\angle \:b = 6\angle \: c = x$

$\angle \:a = \frac{x}{3} \\ \\ \angle \:b = \frac{x}{4} \\ \\ \angle \: c = \frac{x}{6}$

Then,

$\frac{x}{3} + \frac{x}{4} + \frac{x}{6} = 180 \degree$

Taking the lcm of 3,4,6 as 12

$\large \frac{4x + 3x + 2x}{12}= 180°$

$\frac{9x}{12} = 180 \degree \\ \\ x = \frac{180 \times 12}{9} \\ \\ x = \frac{2160}{9} \\ \\ x = 240 \degree$

Measurement Of Angles:-

$\red{ \angle a} = \frac{x}{3} = \frac{240}{3} = 80 \degree \\ \\ \red{ \angle b} = \frac{x}{4} = \frac{240}{4} = 60 \degree \\ \\ \red{ \angle c} = \frac{x}{6} = \frac{240}{6} = 40 \degree$

Hence,The measure of all 3 angles are 80°, 60° and 40°.