In a Triangle LMN, ∠L=2∠M=3∠N then ∠N= ?. The answer should be out of these 4. (a) 18° (b)90° (c) 98 2/11° (d) 32 8/11°
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In a triangle , ∆LMN,
∠L = 2∠M = 3∠N
Let ∠L = x ,
then ∠M = x/2 and ∠N = x/3
we have to find ∠N = ?
we know,
sum of all angles of any triangle be 180°
so, in case of ∆LMN,
∠L + ∠M + ∠N = 180°
x + x/2 + x/3 = 180°
(6x + 3x + 2x)/6 = 180°
11x/6 = 180°
x = 180 × 6/11 = 1080/11°
so, ∠N = x/3 = 1080/(11 × 3) = 360/11° = 32 8/11 °
hence, option (d) is correct.
∠L = 2∠M = 3∠N
Let ∠L = x ,
then ∠M = x/2 and ∠N = x/3
we have to find ∠N = ?
we know,
sum of all angles of any triangle be 180°
so, in case of ∆LMN,
∠L + ∠M + ∠N = 180°
x + x/2 + x/3 = 180°
(6x + 3x + 2x)/6 = 180°
11x/6 = 180°
x = 180 × 6/11 = 1080/11°
so, ∠N = x/3 = 1080/(11 × 3) = 360/11° = 32 8/11 °
hence, option (d) is correct.
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