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In a Δ ABC, (1 / 2) ∠A + (1 / 3) ∠C + (1 / 2) ∠B = 80°, then what is the value of ∠C?
- a)35°
- b)40°
- c)60°
- d)70°
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In a Δ ABC, (1 / 2) ∠A + (1 / 3) ∠C + (1 / 2) ∠B = 8...
Given that,
(1 / 2) ∠A + (1 / 3) ∠C + (1 / 2) ∠B = 80�
⇒ 3∠A + 2∠C + 3∠B = 480�
⇒ 3(∠A + ∠B) + 2∠C = 480� ....(i)
Also, in ΔABC,
∠A + ∠B + ∠C = 180�
On multiplying both sides L.H.S. & R.H.S. by 3, we get
3(∠A + ∠B) + 3∠C = 540� ..... (ii)
On subtracting Eq. (i) from Eq. (ii), we get
∠C = 60�.
Hence, option C is correct.
(1 / 2) ∠A + (1 / 3) ∠C + (1 / 2) ∠B = 80�
⇒ 3∠A + 2∠C + 3∠B = 480�
⇒ 3(∠A + ∠B) + 2∠C = 480� ....(i)
Also, in ΔABC,
∠A + ∠B + ∠C = 180�
On multiplying both sides L.H.S. & R.H.S. by 3, we get
3(∠A + ∠B) + 3∠C = 540� ..... (ii)
On subtracting Eq. (i) from Eq. (ii), we get
∠C = 60�.
Hence, option C is correct.
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In a Δ ABC, (1 / 2) ∠A + (1 / 3) ∠C + (1 / 2) ∠B = 8...
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