The completed statements are:
5. If the measure of ∠1 = 160°, then the measure of ∠5 = 160°.
The reason is the corresponding angles theorem, which asserts that "when a line intersects two parallel lines, the corresponding angles in the two intersection regions are congruent."
6. If the measure of ∠6 = 37°, then the measure of ∠4 = 37°.
The Vertical Angles Theorem, that states the angles that are vertically created by two crossing straight lines, are congruent.
7. If the measure of ∠8 = 82°, then the measure of ∠3 = 98°.
By the Same Side Interior Angles Theorem, when a transversal connects two parallel lines, the interior angles on the same side are supplementary.
∠8 + ∠5 = 180°
∠5 = 180° - 82° = 98°
And by Vertical Angles Theorem,
∠5 = ∠3 = 98°
8. If the measure of ∠4 = 60°, then the measure of ∠5 = 120°.
The total of angles on a straight line is 180°.
∠4 + ∠5 = 180°
∠5 = 180° - 60°
∠5 = 120°
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