GATE CS 2020 Q.9 (GA Q.9): Quantitative Aptitude

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 X-axis, then $\alpha + \beta$ is _______.

$60^\circ$

$90^\circ$

$120^\circ$

$180^\circ$

Official answer and solution

Official answer: B
From: Official GATE 2020 answer key

Solution

Use the relation between slopes and inclinations of perpendicular lines in a plane.

Let line $L_1$ have inclination $\theta_1$ and line $L_2$ have inclination $\theta_2$ measured counterclockwise from the positive X-axis. Because the lines are perpendicular, their inclinations differ by $90^\circ$ , so $\theta_2 = 90^\circ + \theta_1$ .

The acute angle made by $L_1$ with the X-axis is $\alpha = \theta_1$ (assuming $0 < \theta_1 < 90^\circ$ ). The acute angle made by $L_2$ with the X-axis is $\beta = 180^\circ - \theta_2 = 180^\circ - (90^\circ + \theta_1) = 90^\circ - \theta_1$ .

Adding the two acute angles:

\alpha + \beta = \theta_1 + (90^\circ - \theta_1) = 90^\circ

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2020 Computer Science and Information Technology (CS)
Question: 9 of 65, printed as GA Q.9
Section: General Aptitude

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