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.

00:07 Let's calculate the angles where the rectangle is intersected by its diagonal.

00:12 We start with the given angle values.

00:17 Remember, the sum of angles in a triangle is always one hundred eighty degrees.

00:23 Let's substitute the correct values and solve for the unknown angle.

00:33 Now, let's isolate the angle in our equation.

00:37 This gives us the size of the remaining angle.

00:46 Remember, alternate angles between parallel lines are equal.

00:53 These angles are also alternate angles.

00:58 And that's how we solve the problem!

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