Question

Using figure 3 at the right, AB II CD and t is not perpendicular to them, which pair of angles are not congruent?

Using figure 3 above, angles 5 and 6 from a linear pair, if m∠6 = 85, find m∠5​

Answer 1

∠5 = 95°

Explanation:

Where the transversal crosses parallel lines at some angle not a right angle, all of the acute angles are congruent, and all of the obtuse angles are congruent. The acute angles are (obviously) not congruent with the acute angles. Any acute angle is supplementary to any obtuse angle.

Since angles 5 and 6 are a linear pair, the angle relationships of the parallel lines are irrelevant. A linear pair of angles is supplementary.

∠6 = 85° . . . . is given

∠5 is shown as obtuse, so its measure is ...

∠5 = 180° -85° = 95°

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Additional comment

85° angles: 2, 3, 6, 7

95° angles: 1, 4, 5, 8

Any angle from the 85° angle list is not congruent with any angle from the 95° angle list. For example, angles 2 and 5 are not congruent.