In a rectangle, a diagonal forms a 36° angle with a side. Find the measure of the angle between the diagonals, which lies opposite to a shorter side.

Question

The measure of angle is______.

Answer 1

There are a couple ways you could do this.

 

Using geometry is the way I'll show you:

 

Draw a generic rectangle and label the four corners ABCD going clockwise from the top left corner. Draw the two diagonals.

You can label the center where the diagonals cross as point E

 

So now define angle ACD as 36 degrees. By alternate interior angles, angle ACD is congruent to BAC is congruent to BDC is congruent to ABD. They are all 36 degrees.

 

Since ABD and BAC are equiangular, they form an isoceles triangle ABE

The sum of the interior angles of a triangle is 180

 

Therefore, angle AEB is 180 - 36 - 36 = 108

 

The angle in question (BEC) is the supplement of angle AEB and therefore 180 - 108 = 72 degrees