Question

in ∆ abc ,c=2b=a+b+20,then find the value of each angle of ∆ abc

Answer 1

The given is c = 2b = a + b +20
we know that
a + b + c = 180 ................(1)
now putting the first value of c in equation (1)
we have
a + b + 2b = 180
a + 3b = 180 .............(2)

now putting the second value of c in equation (1) we have

a + b + a + b + 20 = 180
2a + 2b = 180 - 20
2(a + b) = 160
a + b = 80 ................(3)

now solving eqn (1) & (2) we have
a + 3b = 180
a + b = 80
(-) (-) (-)
0 + 2b = 100
b = 50

also it is given that c = 2b
so c = 2×50
c = 100
now putting the value of b in eqn (3)
a + b = 80
a + 50 = 80
a = 80 - 50
a = 30

so the values of are :
a = 30
b = 50
c = 100

now check whether the values are correct or not
so we know that sum of all interior angles of a triangle is 180

it means
a + b + c = 180
now putting the value of a, b and c and consider L.H.S
30 + 50 + 100
180
so L.H.S = R.H.S

so these values are correct