Question

Which pair of angles provides a counterexample to the statement: "If two angles are supplementary, then they form a linear pair"?

A. ∠A = 90 degrees and ∠B = 90 degrees.
B. ∠X = 180 degrees and ∠Y = 90 degrees.
C. ∠P = 120 degrees and ∠Q = 60 degrees.
D. ∠M = 60 degrees and ∠N = 120 degrees.
E. ∠C = 150 degrees and ∠D = 30 degrees.

Answer 1

The pair of angles that provides a counterexample to the statement: 'If two angles are supplementary, then they form a linear pair' is ∠M = 60 degrees and ∠N = 120 degrees.

Step-by-step explanation:

The pair of angles that provides a counterexample to the statement: 'If two angles are supplementary, then they form a linear pair' is option D. ∠M = 60 degrees and ∠N = 120 degrees.

A linear pair of angles is a pair of adjacent angles whose measures add up to 180 degrees. In option D, the angles ∠M and ∠N are not adjacent, and their measures add up to 180 degrees, but they do not form a straight line, making them an example that counteracts the given statement.

Therefore, option D is the correct answer.