I DI BUL) of the following questions:
1. In a AABC, if 3angleA = 4angleB = 6angleC then A:B:C = ?
(a) 3:4:6 (b) 4:3:2
(c) 2:3:4
(d) 6:4:3
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Answer:
Given parameters
In ΔABC,
3∠A = 4∠B= 6∠C
Let us consider x = 3∠A = 4∠B = 6∠C
x = 3∠A
∠A = x/3………………….(1)
x = 4∠B
∠B = x/4…………………..(2)
x = 6∠C
∠C = x/6…………………….(3)
By using angle sum property
∠A + ∠B + ∠C = 1800
Put the values of ∠A, ∠B, ∠C
x/3 + x/4 + x/6 = 1800
Let us find the L.C.M of 3,4,6 i.e 12
(4x + 3x + 2x)/12 = 1800
9x = 2160
x = 2400
Substitute the value of x in eqaution (1), (2) and (3)
∠A= x/3
∠A= 240/3 = 80°
∠B= x/4
∠B= 240/4= 60°
∠C= x/6
∠C= 240/6 = 40°
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