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question 4
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which statement about the angles in this diagram is false?
select one:
a. <f = <a
b. <e = <f
c. <d = <c
d. <a = <b

Explanation:

Step1: Recall angle - relationship rules

When two parallel lines are cut by a transversal, vertical angles are equal, corresponding angles are equal, and alternate - interior angles are equal.

Step2: Analyze option a

\(\angle f\) and \(\angle a\) are vertical angles. Vertical angles are always equal. So, \(\angle f=\angle a\).

Step3: Analyze option b

\(\angle e\) and \(\angle f\) are a linear - pair. A linear - pair of angles are supplementary (\(\angle e+\angle f = 180^{\circ}\)), not equal. So, the statement \(\angle e=\angle f\) is false.

Step4: Analyze option c

\(\angle d\) and \(\angle c\) are vertical angles. Vertical angles are equal, so \(\angle d=\angle c\).

Step5: Analyze option d

\(\angle a\) and \(\angle b\) are corresponding angles. Since the lines are parallel, corresponding angles are equal, so \(\angle a=\angle b\).

Answer:

B. \(\angle e=\angle f\)