A)
the sum of all interior angles on any polygon is 180( n - 2 ), where is n = sides in the polygon.
now, this is a quadrilateral, so it has 4 sides, so the sum of all interior angles in degrees for it will be 180( 4 - 2), namely 360°, we know the angle at B is 90°, thus
[tex]\bf \stackrel{B}{90}+\stackrel{A}{2x}+\stackrel{D}{3x}+\stackrel{C}{x}~~=~~360\implies 90+6x=360\implies 6x=270 \\\\\\ x = \cfrac{270}{6}\implies x = 45[/tex]
B)
well, if we dilate or blow up the quadrilateral, the angles always remain the same, same if we shrink it, now, points A and B are colinear, they're lying on the same line, we know B is 90°, hmmm what is A anyway? well, A is 2x, but we know x = 45, thus A is 2(45) = 90°.
since the angle at A is 90° and the angle at B is 90°, and both stem from the same colinear line, the lines AD and BC are perpendicular to AB and also parallel lines, no matter how you scale them, down or up.
