Question

In a triangle ABC,if 3angle A=4angle B=6angle C, calculate the angle

Answer 1

Answer:ok

Step-by-step explanation:

Given:

In ∆ABC , 3∠A= 4∠B= 6∠C

Let x= 3∠A= 4∠B= 6∠C

X=3∠A

∠A= x/3

X=4∠B

∠B= x/4

X=6∠C

∠C= x/6

By angle sum property

∠A+∠B+∠C= 180°

Put the value of ∠A, ∠B, ∠C

X/3+x/4+x/6= 180°

L.c.m of 3,4,6 = 12

(4x + 3x +2x) /12 = 180°

9x = 12 × 180

X= (12× 180) /9

X= 240°

∠A= x/3

∠A= 240/3 = 80°

∠B= x/4

∠B= 240/4= 60°

∠C= x/6

∠C= 240/6 = 40°

_____________________________

Hence the angles be

∠A=80°

∠B=60°

∠C= 40°

_____________________________

Hope this will help you.....

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°.