The side BC of ∆ABC is produced to a point D. If AC = BC and ∠BAC = 70°, then find the value of ∠ACD − ∠ABC.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 70°.
AC = BC and ∠ BAC = 70°
∠ABC = 70°
The sum of angles in a triangle is 180°
∠BAC + ∠ABC + ∠ACB = 180°
⇒ 70° + 70° + ∠ACB = 180°
⇒ ∠ACB = 180° - 140° = 40°
The exterior angle equals the sum of the two opposite interior angles.
⇒ ∠ACD = ∠BAC + ∠ABC = 70° + 70° = 140°
⇒ ∠ACD - ∠ABC = 140° - 70° = 70°
Therefore, the required value is 70°.