Line M is perpendicular to plane B. If line M is in plane A, then which statement must be true

Question

here are the options to the question a)planes A and B are parallel b)line M is perpendicular to plane A c)planes A and B are oblique d)planes A and B are perpendicular

Answer 1

The correct answer is (d), planes A and B are perpendicular.  

 

Since M is perpendicular to plane B, there is at least one line in plane B perpendicular to M and intersecting with M by definition. Since M is in plane A, and the definition of the angle between two planes is the angle between any two intersecting lines perpendicular to the line which is the intersection of the two planes, the angle between the two planes is 90 degrees.  This makes the planes perpendicular by definition.