Question

A, B, C are three angles of a Triangle if A-B=25° and B-C = 10° then angle B is​

Answer 1

Answer:

A−B=15∘            .

B−C=30∘

B=C+30∘         

On adding both equation, we get

A−C=45∘

A=C+45∘         

In a triangle,

A+B+C=180∘         .

Substituting the value from equation (1) and (2), we get

C+45∘+C+30∘+C=180∘

3C=105∘

∠C=35∘.

Substituting this value in equation (1) and (2), we get

∠B=65∘

∠A=80∘

Hence, the angles are ∠A=80∘ ∠B=65∘  ∠C=35∘. 

Answer 2

SOLUTION

GIVEN

A , B , C are three angles of a Triangle

A - B = 25° and B - C = 10°

TO DETERMINE

The angle B

EVALUATION

Here it is given that A , B , C are three angles of a Triangle

So we have

A + B + C = 180° - - - - (1)

A - B = 25° - - - - - - - - (2)

B - C = 10° - - - - - - - - - (3)

Equation 2 - Equation 3 gives

A - 2B + C = 15° - - - - - (4)

From Equation 1 we get

A + C = 180° - B

From Equation 4 we get

180° - B - 2B = 15°

⇒ 3B = 165°

⇒ B = 55°

From Equation 2 we get

A = 25° + 55° = 80°

From Equation 3 we get

C = 55° - 10° = 45°

FINAL ANSWER

A = 80° , B = 55° , C = 45°

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