Question : The side $BC$ of a triangle $ABC$ is extended to $D$. If $\angle ACD = 120^{\circ}$ and $\angle ABC = \frac{1}{2} \angle CAB$, then the value of $\angle ABC$ is:
Option 1: $80^{\circ}$
Option 2: $40^{\circ}$
Option 3: $60^{\circ}$
Option 4: $20^{\circ}$

Question

Question : The side $BC$ of a triangle $ABC$ is extended to $D$. If $\angle ACD = 120^{\circ}$ and $\angle ABC = \frac{1}{2} \angle CAB$, then the value of $\angle ABC$ is:

Option 1: $80^{\circ}$

Option 2: $40^{\circ}$

Option 3: $60^{\circ}$

Option 4: $20^{\circ}$

Team Careers360 · Accepted Answer

Correct Answer: $40^{\circ}$

Solution :
Given that $\angle ACD = 120^\circ$ and $\angle ABC = \frac{1}{2} \angle CAB$
Let $\angle ABC = x$, Then $\angle CAB = 2x$
An exterior angle of a triangle is equal to the sum of opposite interior angles.
So, $\angle ACD = \angle ABC + \angle CAB$
⇒ $120^\circ = x + 2x$
⇒ $3x = 120^\circ$
$ herefore x = 40^\circ$
Hence, the correct answer is $40^\circ$.

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Question : The side BC of a triangle ABC is extended to D. If ∠ACD=120∘ and ∠ABC=12∠CAB, then the value of ∠ABC is:Option 1: 80∘Option 2: 40∘Option 3: 60∘Option 4: 20∘

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Question : The side $B C$ of a triangle $A B C$ is extended to $D$ . If $∠ A C D = 120^{\circ}$ and $∠ A B C = \frac{1}{2} ∠ C A B$ , then the value of $∠ A B C$ is:
Option 1: $80^{\circ}$
Option 2: $40^{\circ}$
Option 3: $60^{\circ}$
Option 4: $20^{\circ}$