Question

The side BC of a triangle ABC is extended to D. If ∠ACD = 120° and ∠ABC = \frac{1}{2} ∠CAB, then the value of ∠ABC is:
[A]20°
[B]80°
[C]40°
[D]60°

Answer 1

Answer:

40° (Option C)

Given:

Triangle ABC and BC extended to D

<ACD=120° and <ABC=1/2<CAB

To find:

Value of <ABC

Solution:-

Let <CAB be x

Then <ABC be 1/2x

Now

$x + \frac{1}{2}x = 120 \: \: \: \: {exterior \: angle \: property}$

$\frac{3x}{2} = 120$

$3x = 240$

$x = 80$

$\frac{1}{2}x = \frac{1}{2} \times 80 = 40$

--------------------

<BAC=80°

<ABC=40°

----- Verifi©ation -----

<ACB=180°-120°

=60°

Now

<A+<B+<BCA =180°

80°+40°+60°=180°

180°=180°

L.H.S=R.H.S