Answer:
m∠DAC = 72°
Explanation:
Figure ABCD is a parallelogram.
As the diagonals BD and AC intersect each other, they form two pairs of vertical angles. Since the vertical angles created by two lines intersecting each other are congruent:
⇒ m∠AFD = m∠BFC = 49°
The interior angles of a triangle sum to 180°. Therefore, for ΔADF:
⇒ m∠DAF + m∠AFD + m∠FDA = 180°
From inspection of the given parallelogram, m∠FDA= 59°.
Therefore, substitute the measures of ∠AFD and ∠FDA into the equation and solve for ∠DAF:
⇒ m∠DAF + 49° + 59° = 180°
⇒ m∠DAF + 108° = 180°
⇒ m∠DAF = 72°
As m∠DAF = m∠ DAC, then m∠DAC = 72°.