Calculate the measure of angle BAC given information about inscribed angles in a circle and a cyclic quadrilateral.

The points D, E, C, B lie on the circle, forming a cyclic quadrilateral BDEC.
We are given:

• $m(\angle ACD) = 30^\circ$. This is an inscribed angle with vertex C on the circle. It subtends arc AD.
• $m(\angle BEC) = 50^\circ$. This is an inscribed angle with vertex E on the circle. It subtends arc BC.

For a cyclic quadrilateral, an exterior angle is equal to the interior opposite angle.