Which of the following are alternate interior angles? Select all that apply.

Option C:  ∠2 and ∠8

Option E: ∠3 and ∠5

Solution:

Two parallel lines cut by a transversal.

Option A: ∠5 and ∠4

∠4 is not interior of parallel lines.

Hence it is not true.

Option B: ∠6 and ∠5

∠6 is not interior of parallel lines.

Hence it is not true.

Option C: ∠2 and ∠8

∠2 and ∠8 lies in the interior of the parallel lines.

∠2 and ∠8 lies in alternate of the transversal line.

Therefore, ∠2 and ∠8 are alternate interior angles.

Hence it is true.

Option D: ∠8 and ∠1

∠1 is not interior of parallel lines.

Hence it is not true.

Option E: ∠3 and ∠5

∠3 and ∠5 lies in the interior of the parallel lines.

∠3 and ∠5 lies in alternate of the transversal line.

Therefore, ∠3 and ∠5 are alternate interior angles.

Hence it is true.

Therefore ∠2 and ∠8, ∠3 and ∠5 are alternate interior angles.

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