Lines containing the lateral sides of trapezoid ABCD with base AD meet point M.

Lines containing the lateral sides of trapezoid ABCD with base AD meet point M. Find angle M if angle A = 65 degrees and angle C = 115 degrees.

Given:

trapezoid ABCD,

foundation AD,

point M – the point of intersection of straight lines AB and MD,

angle A = 65 degrees,

angle C = 115 degrees.

Find the angle M -?

Solution:

Consider the trapezoid ABCD. Its bases BC and AD are parallel, then angle A + angle B = 180 degrees, then angle B = 180 – 65 = 115 (degrees).

The angle MBC and angle ABC are adjacent, then the angle MBC = 180 – 115 = 65 (degrees).

The angle of the MCB and the angle DCB are adjacent, then the angle of the MCB = 180 – 115 = 65 (degrees).

Hence the angle M = 180 – 65 – 65 = 115 – 65 = 50 (degrees).

Answer: 50 degrees.