Find ∠CAD in a Right Triangle with 61° and 17° Angles

Question

ΔABD is a right-angled triangle.

$∢\text{CAD}=\text{?}$

00:00 Find angle CAD

00:05 The sum of angles in a triangle equals 180

00:18 Let's gather terms and isolate A

00:41 This is angle A

00:47 Part of the angle equals the total angle minus the second part

01:04 And this is the solution to the question

If we look at triangle ABD, we can see that we are given two angles: 90° and 17°.

Since the sum of all angles in a triangle equals 180°, we can calculate angle BAD as follows:

$180-90-17=73$

Since we know angle BAC, we can calculate angle CAD as follows:

$73-61=12$

12°