Question

In a triangle ABC, A -B = 33° and B-C = 18°. Find measure of all angles.

Answer 1

Given A-B = 33
So A = 33+B.........(i)

B-C = 18
C = B-18...........(ii)

In a triangle
A+B+C = 180
33+B+B+B-18 = 180 ( FROM i and ii)
3B+15 = 180
3B = 165
B = 165/3
B = 55

From i
A = 33+B
A = 33+55
A = 88

From ii
C = B -18
C = 55-18
C = 37

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Answer 2

A+B+C = 180.....(i)
A-B = 33
A = B + 33......(ii)

B-C = 18
B = C + 18...(iii)
(iii) in (ii)
A = C + 18 + 33 = C + 51....(iv)
(iv) and (iii) in (i)
C + 51 + C + 18 + C = 180
3C = 180 - 51 - 18 = 111
C = 37 degree
A = C + 51 = 37+51 = 88 degree
B = C + 18 = 37 + 18 = 55 degree
A = 88 deg ; B = 55 deg ; C = 37 deg
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