Question

15. If m arc BY = 40 degrees, what is m angle YAC? the figure is not drawn to scale.

Answer 1

If $m\widehat{BY}=40^\circ$, then the central angle $\angle BOY$ has the same measure, and by the inscribed angle theorem we have

$m\angle BAY=\dfrac12m\angle BOY=20^\circ$

It's impossible to know what the measure of angle YAC is from this information alone, but assuming AC is tangent to the circle, then angles BAY and YAC are complementary, so that $m\angle YAC=70^\circ$.