Question

In a triangle ABC, if 2 anglesA = 3 anglesB = 6 anglesC, calculate anglesA, anglesB and anglesC.​

Answer 1

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★Given:

2∠A = 3∠B = 6∠C

★Find:

Measures of ∠A, ∠B and ∠C

★Solution:

F1st we will find the value of both ∠A and ∠B

⇢2∠A = 6∠C..........《Given》

⇢∠A = 6∠C/2

⇢∠A = 3∠C...........➊

Now,

↣3∠B = 6∠C..........〈Given〉

↣∠B = 6∠C/3

↣∠B = 2∠C............➋

we, know that

➩ ∠A + ∠B + ∠C = 180°...........[Angle Sum Property]

where,

∠A = 3∠C [Eq. ➊]

∠B = 2∠C [Eq. ➋]

✬ Substituting these values:

➩ ∠A + ∠B + ∠C = 180°

➩ 3∠C + 2∠C + ∠C = 180°

➩ 6∠C = 180°

➩ ∠C = 180/6

➩ ∠C = 30°

So, ∠C is equal to 30°

Now, using this value of in ∠C eq. ➊

➨ ∠A = 3∠C

➨ ∠A = 3(30)

➨ ∠A = 90°

So, ∠A is equal to 90°

Now, using value of ∠C in eq. ➋

➤ ∠B = 2∠C

➤ ∠B = 2(30)

➤ ∠B = 60°

So, ∠B is equal to 60°

⠀⠀⠀⠀⠀ ________________________

Hence,

❍∠A = 90°

❍∠B = 60°

❍∠C = 30°

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Answer 2

Answer:

Step-by-step explanation:

Angle A=a Angle B=b Angle C=c(suppose)

then 2a=3b a=3b/2

Similarly, 6c=3b c=1/2 b

By angle sum property,

a+b+c=180

3b/2+b=1/2b=180

Substituting the upper values. Further u can simplify this to get the value of b and then the value of a and c also