In Figure 5.65 two parallel lines l and m are being intersecting by a transversal n at points G and H. Then angles thus formed are marked.

If ∠1 is an acute angle then state which of the following statements is false-

From the above list of statements let us evaluate each of the statements separately.

For statement A,

∠ 1 and ∠ 2 forms a linear pair and hence their sum has to be 180°. So this statement is correct.

For statement B,

∠ 2 and ∠ 5 are interior angles lying at the same side of the transversal and hence their sum has to be 180°.

So this statement is correct.

For statement C,

∠ 3 and ∠ 8 are interior angles lying at the same side of the transversal and hence their sum has to be 180°.

So this statement is also correct.

For statement D,

L and M are parallel to each other.

So ∠ 2 and ∠ 6 are corresponding angles and they are equal which implies that their sum is not 180°.

So this statement is false.

So the correct answer is D.