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Two straight lines are drawn perpendicular to each other in $X-Y$ plane. If $\alpha$ and $\beta$ are the acute angles the straight lines make with the $\text{X-}$ axis, then $\alpha + \beta$ is ________.

  1. $60^{\circ}$
  2. $90^{\circ}$
  3. $120^{\circ}$
  4. $180^{\circ}$
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4 Answers

Best answer
15 votes
15 votes

Here, we can clearly see that Two Lines $L_{1}$ and $L_{2}$ are intersecting each other at the right angle.

Now we also know that in a triangle, the sum of three angles is 

  • $\angle A + \angle B + \angle C=180^{\circ}$ 
  • $\alpha +\beta + 90^{\circ}=180^{\circ}$ 
  • $\alpha + \beta = 90^{\circ}$

The answer is (B).

edited by
4 votes
4 votes

L1 and L2 are two perpendicular lines(i.e. 90°).

let say lines L1 and L2 are making acute angles with the x-axis i.e. α and y-axis i.e. β respectively.

therefore, by Angle Sum Property of Triangles in the triangle with 

α+β+90° = 180°

α+β = 90° .

option B.

 

2 votes
2 votes
as the two lines are perpendicular to each other so

90+a+b=180

or, a+b=180-90=90

ans..B
Answer:

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