Question

a. p + q = 7
b. q - p = 7
c. p - q = 7
d. -q - p = 7
(there is a diagram with lines intersecting at point b, a right angle (90°) marked, and points a and c on the lines.)

Explanation:

Step1: Analyze the diagram

The diagram shows two lines intersecting at point B, with a right angle (90°) indicated. Let's assume the angles formed are related to \( p \) and \( q \). Since there's a right angle, the sum or difference of the angles should relate to 90°, but the options have 7, so maybe there's a typo or context missing. Wait, maybe the angles around point B: if one angle is \( p \) and another is \( q \), and the right angle implies a relationship. Wait, the options are about \( p \) and \( q \) equaling 7. Let's check the options:

Option A: \( p + q = 7 \) – not likely if there's a right angle.

Option B: \( q - p = 7 \) – possible if \( q > p \).

Option C: \( p - q = 7 \) – if \( p > q \).

Option D: \( -q - p = 7 \) – negative sum, unlikely.

Wait, maybe the diagram has angles where the difference is 7. Let's assume that the two angles (excluding the right angle) have a difference of 7. If \( q \) is larger than \( p \), then \( q - p = 7 \), which is option B.

Step2: Evaluate the options

• Option A: Sum is 7, but with a right angle, sum should be more, so no.
• Option B: \( q - p = 7 \) – plausible if \( q \) and \( p \) are angles with a difference of 7.
• Option C: \( p - q = 7 \) – would mean \( p > q \), but if the right angle is involved, maybe \( q \) is larger.
• Option D: Negative sum, impossible as angles are positive.

So the most probable is option B.

Answer:

B. \( q - p = 7 \)