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Explanation:
In a ΔABC , ∠C = 3∠B = 2(∠ A + ∠ B ) . Find the angles .
→ let ∠a = x° and ∠b = y°
Then
∠C= 3∠B= 3(y°)
Now,
→ ∠C = 2(∠A+∠B)
=> 3y = 2(x+y)
=> 2x - y = 0............(1)
we know that the sum of angles of triangle is 180°
.°. ∠A + ∠B + ∠C = 180°
=> x + y + 3y = 180
=> x + 4y = 180...........(2)
on multiplying (1) by 4 and adding result with (2), we get
8x + x = 180
= 9x = 180
=> x = 180/9
=> x = 20
putting x = 20 in equation (1)
we get
→ y=(2×20)
→ y=40
thus,
x=20
y=40
Hence
→ ∠a = 20°
→ ∠a = 20° → ∠b=40°
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