PROBLEM ON GEOMETRY –
Example.1) In a Δ ABC, ∠C = 3∠B = 2(∠A + ∠B). Find the angles
Ans.) Let, ∠A = x⁰ and ∠B = y⁰
Then, ∠C = 3∠B = (3 y)⁰
Now, ∠A + ∠B + ∠C = 180⁰
=> x + y + 3 y = 180
=> x + 4 y = 180 ………………….(i)
Also, ∠C = 2 (∠A + ∠B)
=> 3 y = 2(x + y)
=> 2 x – y = 0 ………………………..(ii)
Multiplying (ii) by 4 and adding the result to (i), we get –
9 x = 180
=> x = 20
Putting x = 20 in (ii), we get y = 40
So, x = 20, and y = 40
Hence, ∠A = 20⁰, ∠B = 40⁰, and ∠C = (3 X 40⁰) = 120⁰ (Ans.)