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To solve this problem, let's analyze the geometry of the intersecting lines and their angles.

We have two distinct lines \(AB\) and \(CD\) intersecting at point \(A\). The measure of \(\angle BAC\) is given as \(47^\circ\). We need to find the measure of \(\angle BAD\).

### Step-by-step Solution:

1. **Understand the Problem Setup:**
   - Since \(AB\) and \(CD\) are distinct lines intersecting at \(A\), they form four angles at this point.
   - \(\angle BAC\) and \(\angle BAD\) are adjacent angles that together form a straight line.

2. **Linear Pair of Angles:**
   - When two lines intersect, the adjacent angles are supplementary. This means the sum of the measures of \(\angle BAC\) and \(\angle BAD\) is \(180^\circ\).
   \[
   \angle BAC + \angle BAD = 180^\circ
   \]

3. **Calculate \(\angle BAD\):**
   - We know that \(\angle BAC = 47^\circ\). Plugging this into the equation:
   \[
   47^\circ + \angle BAD = 180^\circ
   \]
   - Solving for \(\angle BAD\):
   \[
   \angle BAD = 180^\circ - 47^\circ = 133^\circ
   \]

### Conclusion:
The measure of \(\angle BAD\) is **133°**.

### Answer: 
The correct choice is **D. 133°**.

Would you like further details or have any questions? Here are some related questions to consider:

1. What are supplementary angles, and how do they relate to intersecting lines?
2. How can we find the measure of vertically opposite angles when two lines intersect?
3. What is the difference between adjacent and vertically opposite angles?
4. How do we apply the concept of linear pairs in different geometric problems?
5. Can angles formed by intersecting lines ever be congruent?

**Tip:** Remember that the sum of the angles around a point is always \(360^\circ\), and adjacent angles formed by a straight line sum to \(180^\circ\).

In a plane, the distinct lines AB and CD intersect at A, where A is between C and D. The measure of ∠BAC is 47°. What is the measure of ∠BAD?

In this problem, we explore how to find the measure of ∠BAD when two distinct lines intersect at A, forming a linear pair. Given that ∠BAC is 47°, we use the supplementary angle theorem to calculate the measure of ∠BAD.

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