Question

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Answer 1

4) ∠3 = ∠2 (VERTICAL ANGLES)

∠2 = ∠16 (ALTERNATE INTERIOR ANGLES)

∠16 = ∠9 (CORRESPONDING ANGLES)

TRUE.

Explanation:

Here, given AD II HJ, GK II CF

Now, to show: ∠3 = ∠9

1. ∠3 = ∠15 (EXTERIOR ANGLES)

∠15 = ∠10 (CORRESPONDING ANGLES)

∠10 = ∠9 (SUPPLEMENTARY ANGLES)

FALSE,as EXTERIOR ANGLES are NOT equal in measure.

2. ∠3 = ∠8 (VERTICAL ANGLES)

∠8 = ∠12 (CORRESPONDING ANGLES)

∠12 = ∠9 (ADJACENT ANGLES)

FALSE, as ∠3 and ∠8 are NOT VERTICAL angles.

3. ∠3 = ∠4 (ADJACENT ANGLES)

∠4 = ∠2 (SUPPLEMENTARY ANGLES)

∠2 = ∠9 (ALTERNATE INTERIOR ANGLES)

FALSE, as ADJACENT ANGLES are NOT equal in measure but their sum is 180°.

4. ∠3 = ∠2 (VERTICAL ANGLES)

∠2 = ∠16 (ALTERNATE INTERIOR ANGLES)

∠16 = ∠9 (CORRESPONDING ANGLES)

TRUE.