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Answer 1 · 2017-10-11T21:34:49

$108$ degrees

Angle ABC = Angle ABD + Angle DBC

Since triangle BCD is equilateral, all of it's angles must be $60$ degrees. So I know that angle DBC is $60$ degrees.

Since triangle ABD is isosceles, angle BAD is the same as angle BDA ( $66$ degrees).

To find angle ABD, we have to use the Triangle Angle Sum Theorem that tells us the interior angles of a triangle add up to $180$ degrees.

So:

$66+66+ABD=180->132+ABD=180->ABD=48$

Thus angle $ABC=48+60=108$