Two straight lines are drawn perpendicular to each other in X−Y plane. If α…
2020
Two straight lines are drawn perpendicular to each other in X−Y plane. If α and β are the acute angles the straight lines make with the X- axis, then α+β is ________ .
- A.
60°
- B.
90°
- C.
120°
- D.
180°
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Correct answer: B
Key idea: if two lines are perpendicular their direction angles differ by 90°, and the acute angle a line makes with the x-axis is the smaller angle between the line and the axis.
Let one line make an acute angle α with the x-axis.
A line perpendicular to it has direction angle α±90°. The acute angle that this perpendicular line makes with the x-axis is 90°−α (because we take the smaller angle with the axis).
Therefore the sum of the two acute angles is α + (90° − α) = 90°.
Answer: 90°
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