Calculate Rectangle Angles: Given 45° Angle CAD Problem

Question

The rectangle ABCD is shown below.

Angle CAD is equal to 45 degrees.

Calculate the remaining angles in the rectangle.

00:00 Calculate the rectangle angles intersected by the diagonal

00:03 The given angle values

00:10 The sum of angles in a triangle equals 180

00:16 Let's substitute appropriate values and solve for the angle

00:26 Let's isolate the angle

00:30 This is the size of the remaining angle

00:39 Alternate angles between parallel lines are equal

00:46 These are also alternate angles

00:51 And this is the solution to the question

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:

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

CAD = BCA = 30
ACD = CAB = 60