Calculate Angle A in a Quadrilateral with Parallel Sides and Diagonals

Question

ABCD is a quadrilateral.

AB||CD
AC||BD

Calculate angle $∢A$ .

00:00 Find angle A

00:05 The sum of angles in a triangle is always equal to 180

00:14 Let's substitute appropriate values according to the given data

00:29 and isolate A

00:48 and this is the solution to the problem

Angles ABC and DCB are alternate angles and equal to 45.

Angles ACB and DBC are alternate angles and equal to 45.

That is, angles B and C together equal 90 degrees.

Now we can calculate angle A, since we know that the sum of the angles of a square is 360:

$360-90-90-90=90$

90°