Side BC of a ABC is extended upto D such that CD = AC. If BAD = 118° and ACB = 80°, then the value of ABC is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 22°.
∠ACB + ∠ACD = 180° [straight line]
⇒ 80 + ∠ACD = 180°
⇒ ∠ACD = 100°
In △ACD, AC = CD
So, ∠CAD = ∠ADC [angle opposite to equal sides are equal]
⇒ ∠ACD + ∠CAD + ∠ADC = 180°
⇒ 100 + 2∠ADC = 180°
⇒ 2∠ADC = 80°
⇒ ∠ADC = 40°
Now, In △ABD
⇒ ∠BAD + ∠ABD + ∠ADB = 180°
⇒ 118° + ∠ABD + 40° = 180°
⇒ ∠ABD = 180° - 158°
⇒ ∠ABD = 22° = ∠ABC
Thus, ∠ABC = 22°