Calculate Angle BAC in a Right Triangle with 147° External Angle

Question

According to the data,

Calculate the size $∢\text{BAC}$

00:00 Find angle A

00:04 Supplementary angle to a straight angle (180)

00:18 The sum of angles in a triangle equals 180

00:25 Let's collect terms and isolate BAC

00:48 And this is the solution to the question

Since we are given an angle of 147, let's calculate the angle ACB which complements it to 180 degrees:

$180-147=33$

Now we have two angles in triangle ABC, and we can calculate angle BAC:

$180-90-33=57$