GMAT Question > In a triangle ABC,∠A = 900, AL is drawn p...

In a triangle ABC,∠ A = 90^{0}, AL is drawn perpendicular to BC, Then ∠ BAL is equal to:

- a)∠ALC
- b)∠ACB
- c)∠BAC
- d)∠B - ∠BAL
- e)None of these

Correct answer is option 'B'. Can you explain this answer?

∠ BAL + ∠ B + 90^{0} = 180^{0}

or, ∠ BAL + ∠ B = 90^{0}

or, ∠ BAL = 90^{0} - ∠ B ----------- (1)

Now, in Δ ABC,

∠ ACB + ∠ B + ∠ A = 180^{0}

∠ ACB = 90^{0}

-∠ B ----- (2)

From, (1) and (2),

∠ BAL = ∠ ACB.

or, ∠ BAL + ∠ B = 90

or, ∠ BAL = 90

Now, in Δ ABC,

∠ ACB + ∠ B + ∠ A = 180

∠ ACB = 90

-∠ B ----- (2)

From, (1) and (2),

∠ BAL = ∠ ACB.

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∠BAL + ∠B + 900= 1800or, ∠BAL + ∠B = 900or, ∠BAL = 900- ∠B ----------- (1)Now, in Δ ABC,∠ACB + ∠B + ∠A = 1800∠ACB = 900-∠B ----- (2)From, (1) and (2),∠BAL = ∠ACB.