Question

In the figure above, if \( m \parallel k \) and \( s = t + 30 \), then \( t = \dots \)

• A. 30
• B. 60
• C. 75
• D. 80
• E. 105

Hint:

When dealing with parallel lines and transversals, always use the corresponding angle or alternate interior angle properties to relate the angles and solve for unknowns.

Answer 1

The Correct Option is D

Step 1: Analyze the parallel lines.
Since \( m \parallel k \), the angles formed by a transversal intersecting these parallel lines are equal. The relationship between the angles allows us to set up an equation involving \( t \).
Step 2: Use the given relationship.
We are given that \( s = t + 30 \). Using this information and the properties of parallel lines, we can solve for \( t \).
Step 3: Solve for \( t \).
After applying the given relationships and solving, we find that \( t = 80 \).
Final Answer: \[ \boxed{\text{The correct answer is (D) 80.}} \]