Is it possible to find such an angle using only angle chasing?

The answer is: It is impossible with only angle chasing. (It may be possible for some limited special cases.)

In general, the angle $∠ACD$ is related to known angles via the sine equation below,

$$\sin (∠ACD )\sin (∠ACD-∠C) = \frac{\sin ( ∠CAD) \sin (∠CBD) \sin (∠DAB)}{\sin (∠B) }$$

For arbitrary triangles ACB and ADB, the above relationship can not be reduced to just angle additions and subtractions.

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A well-known geometry problem pertinent to the topic here is the so-called the "hardest easy angle question" below:

enter image description here

Tags:

Geometry

Angle

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