Given two parallel lines cut by a transversal, if the alternate interior angles are $k-10$ degrees and $2k-40$ degrees, what is the value of $k$?

• A. $60$
• B. $40$
• C. $30$
• D. $50$

Answer: (D)

Verified step by step guidance

1. Recall that when two parallel lines are cut by a transversal, alternate interior angles are congruent (equal in measure). This means we can set the two given angle expressions equal to each other.
2. Write the equation based on the equality of alternate interior angles: \(k - 10 = 2k - 40\).
3. To solve for \(k\), first get all terms involving \(k\) on one side and constants on the other. Subtract \(k\) from both sides: \(-10 = k - 40\).
4. Next, add 40 to both sides to isolate \(k\): \(-10 + 40 = k\), which simplifies to \$30 = k$.
5. Verify the solution by substituting \(k = 30\) back into the original angle expressions to ensure both angles are equal, confirming the correctness of the value.