Find Angle ABC in a Rectangle with 30-Degree Reference Angle

Question

ABCD is a rectangle.

$∢\text{ABC}=?$

00:00 Calculate angle ABC

00:04 The sum of angles in a triangle equals 180

00:20 Let's collect terms and isolate ABC

00:38 And this is the solution to the question

Since we know that ABCD is a rectangle, we know that AC is parallel to BD.

Therefore, angles ACB and CBD are equal (30 degrees).

In a rectangle, we know that all angles are equal to 90 degrees, meaning angle ABD is equal to 90.

Now we can calculate angle ABC as follows:

$90-30=60$