Question

fill in the blanks to complete the sentences. then find the measures of the marked angles and give reasons.
angles associated with parallel lines
1.
2 pairs of corresponding angles: a and __, c and __
if ( ab parallel cd ), then
( a = ) __ and ( c = ) __
2.
2 pairs of alternate angles: e and __, g and __
if ( ab parallel cd ), then
( e = ) __ and ( g = ) __
3.
2 pairs of interior angles: m and __, p and __
if ( ab parallel cd ), then
( m + ) ____ ( = 180^circ ) (m & n - supplementary angles)
( p + ) ____ ( = 180^circ ) (p & q - supplementary angles)
4.
( c = 180^circ - 132^circ ) (interior angles)
( = ) ____

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Explanation:

Part 1: Corresponding Angles

Step1: Identify corresponding angles

Corresponding angles are in the same position relative to the parallel lines and transversal. For lines \(AB \parallel CD\) with transversal, angle \(a\) corresponds to \(b\), and angle \(c\) corresponds to \(d\). By the Corresponding Angles Postulate, if \(AB \parallel CD\), then \(a = b\) and \(c = d\).

Step1: Identify alternate angles

Alternate angles are on opposite sides of the transversal, inside (or outside) the parallel lines. Angle \(e\) is alternate to \(b\), and angle \(g\) is alternate to \(f\). By the Alternate Angles Theorem, if \(AB \parallel CD\), then \(e = b\) and \(g = f\).

Step1: Identify interior angles

Interior angles are between the parallel lines. Angle \(m\) is interior with \(n\), and angle \(p\) is interior with \(q\). By the Consecutive Interior Angles Theorem, if \(AB \parallel CD\), then \(m + n = 180^\circ\) (supplementary) and \(p + q = 180^\circ\) (supplementary).

Answer:

2 pairs of corresponding angles: \(a\) and \(b\), \(c\) and \(d\)
If \(AB \parallel CD\), then \(a = b\) and \(c = d\)

Part 2: Alternate Angles