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in Linear Equations by (49.2k points)
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In a triangle ABC, ∠A= xº,∠B = yº and ∠C = (y+20)º . If 4x – y = 10, then the triangle is 

(a) Right angled 

(b) Obtuse angled 

(c) Equilateral 

(d) None of these

1 Answer

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by (53.1k points)
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Best answer

(a) Right angled

By the angle sum property of a triangle, 

∠A + ∠B + ∠C = 180º

\(\Rightarrow\)x + y + y + 20° = 180° \(\Rightarrow\) x + 2y = 160 .............(i)

Given, 4x – y = 10  .................(ii)

Multiplying (ii) by 2, we get 

8x – 2y = 20 ...........…(iii) 

Adding eqn (i) and (iii),

9x = 180 \(\Rightarrow\) x = 20

\(\therefore\) From (i), 2y = 160 – 20 = 140 \(\Rightarrow\) y = 70

\(\Rightarrow\) ∠A = 20º , ∠B = 70º , ∠C = 90º

\(\therefore\) The triangle is right angled.

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