The inscribed angle theorem says that the measure of angle BDC is 2 times larger than the measure of angle BAC.
Angle CBD has measure 44 degrees, and we're told angles CBD and BCD are congruent. This means triangle BCD is isosceles.
The interior angle measures of any triangle add up to 180 degrees, so the measure of angle BDC must be
[tex]m\angle BDC=180^\circ-2(44^\circ)=92^\circ[/tex]
Then [tex]m\angle BAC=\dfrac{92^\circ}2=46^\circ[/tex].
