XYAB is a rectangleFind m < XDY X Y 55 deg D A B
To find m < XDY, we need to determine the measure of the angle formed by points X, D, and Y within the given rectangle XYAB.
Since XYAB is a rectangle, we know that opposite sides are congruent and parallel. Therefore, angle XAB is congruent to angle XYB and angle XDA is congruent to angle XDY.
From the given information, we know that angle XYA measures 55 degrees. Since angle XAB and angle XYB are congruent, each of them will measure 55 degrees as well.
Since the sum of the interior angles of a rectangle is 360 degrees, we can subtract the measures of the angles we know to find the measure of angle XDA.
360 - 55 - 55 - 90 = 160 degrees
Therefore, angle XDA measures 160 degrees. Since angle XDA and angle XDY are congruent, m < XDY is also 160 degrees.