The side BC of ∆ABC is produced to a point D. If AC = BC and ∠BAC = 70°, then find the value of 2.5∠ACD − 1.5∠ABC.
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Correct answer: A
Explanation
The correct answer is option 1 i.e. 245°.
AC = BC and ∠BAC = 70°
Triangle ABC is isosceles.
So, ∠ABC = ∠BAC = 70°
The sum of angles in a triangle is 180°.
∠BAC + ∠ABC + ∠ACB = 180°
⇒ 70° + 70° + ∠ACB = 180°
⇒ ∠ACB = 180° - 140° = 40°
A triangle's exterior angle equals the sum of the two opposite interior angles.
∠ACD = ∠BAC + ∠ABC = 70° + 70° = 140°
Now, 2.5∠ACD - 1.5∠ABC = 2.5 × 140° - 1.5 × 70° = 350° - 105° = 245°
Therefore, the value of 2.5∠ACD - 1.5∠ABC is 245°.