Question

I need help with these .

Answer 1

1. 102°
2. 56°
3. 104°
4. 138°
5. 95°
6. 133°

Explanation:

It is helpful to remember the names and relationships of angles where a transversal crosses parallel lines. Here you have ...

alternate exterior angles (fig 1) (congruent) . . . x = 102°

corresponding angles (fig 2) (congruent) . . . x = 56°

consecutive interior angles (fig 3) (supplementary) . . . x = 180° -76° = 104°

vertical angles (fig 4) (congruent) . . . x = 138°

consecutive exterior angles (fig 5) (supplementary) . . . x = 180° -85° = 95°

alternate interior angles (fig 6) (congruent) . . . x = 133°

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Additional comment

In most of these figures, the angles are obviously either acute or obtuse. Where a transversal crosses parallel lines, all of the obtuse angles are congruent, and all of the acute angles are congruent. The obtuse and acute angles are supplementary.