Question

If m angle B= m angle D=42 find m angle C so that quadrilateral ABCD is a paralllogram

Answer 1

Since the sum of all the angles of a quadrilateral must equal 360, and opposite angles of a parallelogram are equal, we can find the angle in question.

angle B and angle D are opposite angles and add up to 84 degrees of the 360 degree total. So, subtracting this sum from 360 degrees tells us the sum of the remaining two angles (angle A and angle C).

Since they must be equal, each will be half of the remainder.