Question

in the given figure ab and ac are opposite rays, if (a-3b)=20°, find anglea and b

Answer 1

it is given that
a+b=180........i
and
a-3b=20

subtracting both equations
a+b-a+3b=180-20
4b=160
b=40
put in i
a=140

Answer 2

The value of ∠a is 140° and ∠b is 40°

GIVEN

AB and AC are opposite rays.

(a-3b) = 20°

TO FIND

∠a and ∠b

SOLUTION

We can simply solve the above problem as follows;

It is given,

AB and AC are opposite rays.

So,

CB is a straight line.

∠DAC = a°

∠DAB = b°

We know that,

∠a + ∠b = 180° (Equation 1) (Angles of straight line are supplimentary)

It is given,

∠a - ∠3b = 20° (Equation 2)

Subtracting Equation 2 from Equation 1

∠a + ∠b - (a - 3b) = 180 - 20

a + b - a + 3b = 160

4b = 160

b = 160/4 = 40°

Putting the value of ∠b in equation 1

∠a + 40 = 180

∠a = 180-40

∠a = 140°

Hence, The value of ∠a is 140° and ∠b is 40°

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