Question

What is the measure of angle \( x \)?

Statement (I): \( PQ \parallel RS \).
Statement (II): Line \( AB \) bisects \( PQ \).

• A. Statement (I) alone is sufficient.
• B. Statement (II) alone is sufficient.
• C. Both statements (I) and (II) are sufficient.
• D. Neither statement is sufficient.

Hint:

Whenever a figure contains parallel lines and a transversal, first look for corresponding angles, alternate interior angles, and supplementary angle pairs before attempting lengthy calculations.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This is an average-based problem. We must determine the teacher's weight using the students' initial average and the updated average after the teacher is added.


Step 2: Key Formula or Approach:
The average is computed as:
\[ \text{Average} = \frac{\text{Sum of all values}}{\text{Total number of values}} \] The teacher's weight equals the new total weight minus the original total weight of the students.


Step 3: Detailed Explanation:
The starting average for 30 students is 40 kg.
\[ \text{Total weight of 30 students} = 30 \times 40 = 1200 \text{ kg} \] Including the teacher raises the total count to \(30 + 1 = 31\) people.
The average rises by 1 kg, making the new average \(40 + 1 = 41\) kg.
\[ \text{Total weight of 31 individuals} = 31 \times 41 \] \[ 31 \times 41 = 1271 \text{ kg} \] Subtracting the initial total from the new total gives the teacher's weight:
\[ \text{Weight of teacher} = 1271 - 1200 = 71 \text{ kg} \]

Step 4: Final Answer:
The correct choice is (B).