Question

question 5
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which pairs of angles are equal in this diagram?
select one:
a. a = b, c = d, and e = f
b. a = e, b = d, and c = g
c. a = e, c = g, and b = f
d. a = c, e = g, and f = h

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. In the given diagram, when two lines intersect, vertical angles are formed. For the top - intersection, $\angle a$ and $\angle d$ are vertical angles, $\angle b$ and $\angle c$ are vertical angles. For the bottom - intersection, $\angle e$ and $\angle h$ are vertical angles, $\angle f$ and $\angle g$ are vertical angles. Also, when two parallel lines are cut by a transversal, corresponding angles are equal. $\angle a$ and $\angle e$ are corresponding angles, $\angle b$ and $\angle f$ are corresponding angles, $\angle c$ and $\angle g$ are corresponding angles, $\angle d$ and $\angle h$ are corresponding angles.

Step2: Analyze each option

Option a only shows vertical - angle equalities within each intersection but not the relationships between the two sets of angles formed by the transversal. Option b has incorrect pairings. Option c is correct as $\angle a$ and $\angle e$ are corresponding angles, $\angle c$ and $\angle g$ are corresponding angles, and $\angle b$ and $\angle f$ are corresponding angles. Option d shows vertical - angle equalities within each intersection but not the correct corresponding - angle relationships.

Answer:

c. $a = e, c = g$, and $b = f$