Question

Determine the value of angle k.
1. Angle k and m lies on a straight line.
2. Angle m = 39°.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
• C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask.
• D. EACH statement ALONE is sufficient to answer the question asked.
• E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hint:

This is a classic example of a Data Sufficiency problem where two pieces of information, each insufficient on its own, combine to solve a system of equations. Statement (1) provides the equation, and Statement (2) provides a value to plug into it.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The question asks for a specific numerical value for angle k. We must determine if the given statements provide enough information to find this single value.

Step 2: Key Formula or Approach:
Angles that lie on a straight line are supplementary. This means their sum is 180°.
If k and m are on a straight line, then \( k + m = 180° \).

Step 3: Detailed Explanation:
Analyze Statement (1): "Angle k and m lies on a straight line."
This tells us the relationship between k and m:
\[ k + m = 180° \] However, since the value of m is unknown, we cannot determine the value of k. This is one equation with two variables. Therefore, Statement (1) is not sufficient.
Analyze Statement (2): "Angle m = 39°."
This statement gives us the value of angle m. It provides no information about angle k or its relationship with m. Therefore, Statement (2) is not sufficient.
Analyze Statements (1) and (2) Together:
From Statement (1), we have the equation: \( k + m = 180° \).
From Statement (2), we have the value: \( m = 39° \).
We can substitute the value of m from the second statement into the equation from the first statement:
\[ k + 39° = 180° \] \[ k = 180° - 39° \] \[ k = 141° \] This gives a unique value for angle k. Therefore, the two statements together are sufficient.

Step 4: Final Answer:
Since neither statement is sufficient on its own, but they are sufficient when combined, the correct option is (C).