Question

in triangle abc if angle A minus angle b is equal to 42 degree and Angle B minus angle C is equal to 21 degree then find b

Answer 1

53°

Step-by-step explanation:

a+b+c=180°,a-b= 42-(1),b-c=21-(2)

now we add (1) and (2) and we get a-c= 63, a=c+63,c=c,b=c+21

so c+63+c+21+c=180

3c= 180-84=96

therefore c=32, b= c+21=32+21= 53°

Answer 2

Angle B is equal to 53°.

Solution: In triangle ABC,

Angle A - Angle B= 42° ----(i)

Angle B - Angle C= 21° -----(ii)

Adding (i) and (ii),

Angle A - Angle C= 63°

=> Angle A= 63° + Angle C----(iii)

Equation (ii) can be written as:

Angle B = 21° + Angle C -----(iv)

" According to the angle sum property of a traingle, the sum of all internal angles of a traingle is equal to 180°."

Therefore,

Angle A+ Angle B + Angle C = 180°

Using (iii) and (iv):

63° + Angle C+ 21° + Angle C+ Angle C= 180°

=> 3× Angle C + 84° = 180°

=> 3 × Angle C = 180° -84°

=> 3 × Angle C = 96°

=> Angle C= 96/3

=> Angle C = 32°

Angle B = 21° + Angle C

=> Angle B = 21° + 32°

=> Angle B = 53°

Therefore, Angle B = 53°