Right Triangle Angle Calculation: Finding ∠CBD with Given 30° Angle

Question

ABC Right triangle

If $∢\text{BAC}=30$

Calculate the size of $∢\text{CBD}$

00:00 Calculate CBD

00:06 The sum of angles in a triangle equals 180

00:16 Let's group terms and isolate C

00:38 This is angle C

00:50 Now let's use exactly the same method in triangle DBC to find A

01:00 Let's group terms and isolate A

01:11 And this is the solution to the question

Note that angle BDA equals 90 degrees, therefore we can deduce that angle BDC also equals 90 degrees.

Let's look at triangle ABC and calculate angle C, since angles A and B are given to us:

$180-90-30=60$

Now let's focus on triangle BDC and calculate angle alpha, since we have calculated the other two angles.

$180-90-60=30$