Question

The difference of the same side angles of two parallel lines is 35°. Find all angles

Answer 1

Answer:

All acute angles are 72.5°; all obtuse angles are 107.5°.

Explanation:

Angles on the same side of a transversal cutting parallel lines have measures that total 180°. If o and a represent the measures of the obtuse and acute angles, respectively, then we have ...

... o + a = 180

... o - a = 35

Adding these two equations gives ...

... 2o = 215

... 215/2 = o = 107.5 . . . . degrees

Then the other angle is ...

... a = 107.5 - 35 = 72.5 . . . . degrees

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All corresponding angles have the same measures. All vertical angles have the same measures. So the 8 angles that arise from the intersection of the transversal with these two parallel lines will have one or the other of these two measures.