Question

a pair of parallel lines is cut by another pair of parallel lines as shown in the figure. which angles are congruent to angle k?

angles p, q, and r
angles m, e, and c
angles g, a, and b
angles d, e, and c
angles m, n, and p

Explanation:

Identify the angle type of angle K

$$ \text{Angle } K \text{ is an obtuse angle.} $$

Identify congruent angles at the same intersection

$$ \text{Angle } K \cong \text{Angle } M \quad (\text{vertical angles}) $$

Identify congruent angles at other intersections using parallel line properties

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Match with the given options

$$ \text{The set of angles congruent to } K \text{ is } \{M, E, C\}. $$

Answer:

• angles P, Q, and R
• angles M, E, and C (Correct answer)
• angles G, A, and B
• angles D, E, and C
• angles M, N, and P