Question

Which statement is true about Angle C P B?

Lines C D and A B intersect at point P.

It is supplementary to Angle A P C.
It is complementary to Angle A P C.
It is congruent to Angle A P C.
It is linear to Angle A P D.

Answer 1

To determine the relationship of Angle \( CPB \) with Angle \( APC \), we can use some fundamental geometric properties regarding angles formed by intersecting lines.

1. **Understanding the Relationships:**
- When two lines intersect, they form four angles around the intersection point.
- Opposite angles are congruent, while adjacent angles formed on the same line are supplementary.

2. **Given Relationships:**
- If Angle \( APB \) and Angle \( APC \) are adjacent angles (they share the vertex \( P \) and a side), then they are supplementary, meaning their measures add up to \( 180^\circ \).

3. **Evaluating the Statements:**
- "It is **supplementary to Angle APC**." — This implies Angle CPB + Angle APC = 180°, which is true if they are adjacent angles.
- "It is **complementary to Angle APC**." — This would mean that their measures add up to \( 90^\circ \), which is not true in the case of intersecting lines (unless such measures were specifically given).
- "It is **congruent to Angle APC**." — This would imply they have the same measure, which is not necessarily true in this context.
- "It is **linear to Angle APD**." — Depending on the exact angles defined, this might not hold, as ‘linear’ could refer to angles being on a straight line that sum to 180, which would be true for adjacent angles, but it’s vague without further context.

Given the most basic principles of geometry regarding intersecting lines, the true relationship based on the provided statements would likely be:

**"It is supplementary to Angle A P C."**

So, the correct answer is: **It is supplementary to Angle A P C.**