Calculate Rectangle Angles: Given 45° Angle CAD Problem

The rectangle ABCD is shown below.

Angle CAD is equal to 45 degrees.

Calculate the remaining angles in the rectangle.

Let's observe triangle CAD, the sum of angles in a triangle is 180 degrees, hence we can determine angle DAC:

$CAD+90+30=180$

$CAD+120=180$

$CAD=180-120$

$CAD=60$

Given that ABCD is a rectangle, all angles are equal to 90 degrees.

Therefore angle CAB equals:

$90-CAD=90-60=30$

Furthermore we can deduce that CAD equals 30 degrees, since ABCD is a rectangle all angles are equal to 90 degrees.

CAB equals 60 degrees.

Therefore:

$CAD=BCA=30,ACD=CAB=60$