In the diagram shown, lines m and n are crossed by transversal line t. Why are m and
n not parallel?

Step-by-step explanation:

If two line 'm' and 'n' are parallel and a transversal line 't' i intersecting these lines at two distinct points,

Sum of interior consecutive angles should be 180°.

(Property of the angles formed between parallel lines and a transversal line)

Therefore, 114° + 64° = 180°

178° = 180°

Which is not true.

Therefore, lines 'm' and 'n' are not the parallel lines.