Side BC of a triangle ABC has been produced to a point D such that ∠ACD = 120°. If ∠B = 1/2 ∠A, then ∠A is equal to
A. 80°
B. 75°
C. 60°
D. 90°
Answers
Given: Side BC of a triangle ABC has been produced to a point D such that ∠ACD = 120° and ∠B = 1/2 ∠A.
To Find : ∠A is equal to
Proof :
By exterior angle theorem, If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles :
∠ACD = ∠A + ∠B
120° = ∠A + ½ ∠A
[Given : ∠B = ½ ∠A]
120° = (2∠A + ∠A)/2
120° × 2 = 3∠A
240° = 3∠A
∠A = 240°/3
∠A = 80°
Hence , ∠A is equal to 80°.
Among the given options option (A) 80° is correct.
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Similar questions :
In Δ ABC, ∠A=50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACD meet at E, then ∠E =
A. 25°
B. 50°
C. 100°
D. 75°
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In a Δ ABC, If ∠A = 60°, ∠B =80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC=
A. 60°
B. 120°
C. 150°
D. 30°
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Answer:
Step-by-step explanation:
∠ACD = ∠A + ∠B
120° = ∠A + ½ ∠A
[Given : ∠B = ½ ∠A]
120° = (2∠A + ∠A)/2
120° × 2 = 3∠A
240° = 3∠A
∠A = 240°/3
∠A = 80°