Question

In the given figure, ∠BAC = 70°, ∠EBC = 140°, then ∠ACD is

• A. 120°
• B. 100°
• C. 110°
• D. 105°

Answer 1

Answer:

C. 110°

Solution: Given: ∠EBC = 140∘ and ∠BAC = 70∘ Concept: Exterior angle: The angle formed between one side of a triangle and the extension of its adjacent side is called the exterior angle.​ Theorem: The exterior angle so formed is equal to the sum of the two interior opposite angles. This is called the exterior angle theorem of the triangle. In the above diagram, ∠A and ∠B represent the interior angle but ∠ACD represents the exterior angle. so according to the exterior angle theorem, ∠ACD = ∠​A + ∠B Calculation: ∵ ∠EBC + ∠ABC = 180∘ ⇒ 140∘ + ∠ABC = 180∘ ⇒ ∠ABC = 180∘ - 140∘ ⇒ ∠ABC = 40∘ .........(1) ∵ ∠ACD = ∠BAC + ∠ABC ∴ ∠ACD = 70∘ + 40∘ (From 1st) ⇒ ∠ACD = 110∘