Question

In ∆ABC, if A - B = 33° and B - C = 18° then angle B =?

Answer 1

In triangle ABC
a-b=33
a=33+b ------------1
b-c=18
c=b-18 ------------2
Now in triangle abc by angle sum property
a+b+c=180
33+b+b+b-18=180 (by 1 and 2)
15+3b=180
3b=180-15
3b=165
b=165/3
b=55
Now put value of b in eq. 1 and 2
a-b=33
a-55=33
a=33+55
a=88
b-c=18
55-c=18
c=55-18
c=37
Your answer is:
a=88
b=55
c=37

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Answer 2

A - B = 33° or A = 33+B

and B - C = 18° or C=B -18

and from angle sum property of∆
A+B+C = 180
33+B+B+B-18 =180

3B =180-15

B=. 165/3 =55°
A= 33+55=88
C=55-18 =37