Question

a road map shows the intersections of roads. there are three parallel roads cut by a fourth road that acts like a transversal.
what is true about the angles formed by the intersecting roads?
choose one option from each drop - down menu to answer the question.
if \\( \angle e b c \\) measures \\( x ^ { \circ } \\), then \\( \angle b e d \\) measures \\( x \\)
\\( \angle h e f \\) has the same measure as \\( \angle \\) choose...
the sum of the measures of \\( \angle g h e \\) and \\( \angle \\) choose... is \\( 180 ^ { \circ } \\).

Explanation:

Step1: Use Alternate Interior Angles

Since the roads are parallel and the trans - verse road acts as a transversal, for the first blank, \(\angle EBC\) and \(\angle BED\) are alternate interior angles. So if \(\angle EBC=x^{\circ}\), then \(\angle BED = x^{\circ}\).

Step2: Use Corresponding Angles

For the second blank, \(\angle HEF\) and \(\angle BED\) are corresponding angles (because of the parallel roads and the transversal).

Step3: Use Consecutive Interior Angles

For the third blank, \(\angle GHE\) and \(\angle CHE\) are consecutive interior angles. The sum of consecutive interior angles formed by a transversal intersecting two parallel lines is \(180^{\circ}\).

Answer:

\(\angle BED\), \(\angle BED\), \(\angle CHE\)