Answer:
m∠BAC = 40°
Explanation:
Note that line BD passes through A, so ∠BAC and ∠CAD form a linear pair. By the Linear Pair Postulate, ∠BAC and ∠CAD are supplementary angles, and by definition their measures add to 180°:
m∠BAC + m∠CAD = 180°
Since the diagram gives us that m∠CAD = 140°, we can substitute and solve:
Starting supplementary angles definition equation ...
m∠BAC + m∠CAD = 180°
Substituting the known value of m∠CAD ...
m∠BAC + (140°) = 180°
Subtracting 140° from both sides of the equation...
(m∠BAC + 140°) - 140° = (180°) - 140°
Simplifying/evaluating...
m∠BAC = 40°