Two straight lines are drawn perpendicular to each other in the X-Y plane. If alpha and beta are the acute angles the straight lines make with the X-axis, then alpha + beta = ? A. 60 degrees B. 90 degrees C. 120 degrees D. 180 degrees

GATE 2020 · General Aptitude · Cartesian Coordinates · medium

Answer: alpha + beta = 90 degrees. Answer: B. 90 degrees.

1. Set up slopes in terms of angles: L1 makes acute angle alpha, so m1 = tan(alpha). Since L2 is perpendicular to L1, m1 * m2 = -1, so m2 = -1/tan(alpha) = -cot(alpha) = -tan(90 - alpha).
2. Find the acute angle beta of L2: Comparing: -tan(beta) = -tan(90 - alpha) => tan(beta) = tan(90 - alpha) => beta = 90 - alpha.
3. Compute the sum: alpha + beta = 90 degrees, regardless of the specific value of alpha.