In a ∆ ABC, if ∠A + ∠B = 135° and ∠C

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In a ∆ ABC, if ∠A + ∠B = 135° and ∠C + 2 ∠B = 180°, then the correct relation is :

1. CA > AB
2. CA = AB
3. CA < AB
4. CA + AB = CB

Correct Option: A

On the basis of question we draw a figure of triangle ABC ,

Given that , ∠A + ∠B = 135°
We know that , ∠A + ∠B + ∠C = 180°
∴ ∠C = 180° – 135° = 45°
∴ ∠C + 2∠B = 180°
∴ 2∠B = 180° – ∠C = 180° – 45° = 135°

∴ ∠B =	135°	= 67.5°
	2

∴ ∠A = ∠B
⇒ BC = AC
∠C < ∠B
⇒ AB < AC