Ex 3.7, 5 (Optional) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

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Ex 3.7, 5 In a ABC, C = 3 B = 2 ( A + B). Find the three angles. Let A = x and B = y Given that C = 3 B C = 3y Also, C = 2 ( A + B) C = 2 (x + y) Applying Angle sum Property A + B + C = 180 For C = 3y Put A = x B = y and C = 3y Since ABC is a triangle, By angle sum property A + B + C = 180 x + y + 3y = 180 x + 4y = 180 For C = 2(x + y) Put A = x B = y and C = 2 (x + y) Since ABC is a triangle, By angle sum property A + B + C = 180 x + y + 2 (x + y) = 180 x + y + 2x + 2y = 180 3x + 3y = 180 3(x + y) = 180 (x + y) = 180/3 x + y = 60 Hence, the equations are x + 4y = 180 (1) x + y = 60 (2) From equation (1) x + 4y = 180 x = 180 4y Put x = 180 4y in equation (2) x + y = 60 180 4y + y = 60 180 60 = 4y y 120 = 3y 3y = 120 y = 120/3 y = 40 Put y = 40 in equation (1) x + 4y = 180 x + (4 40) = 180 x + 160 = 180 x = 20 Thus, A = x = 20 B = y = 40 C = 3y = 3 40 = 120