Question

corresponding angles postulate
if two parallel lines are cut by a transversal,
then the pairs of corresponding angles are _.
wording for proof:
alternate interior angles theorem
if two parallel lines are cut by a transversal,
then the pairs of alternate interior angles are _.
wording for proof:
alternate exterior angles theorem
if two parallel lines are cut by a transversal,
then the pairs of alternate exterior angles are _.
wording for proof:
consecutive interior angles theorem
if two parallel lines are cut by a transversal,
then the pairs of consecutive interior angles are _.
wording for proof:
example 2: find each angle measure and write the relationship.
m∠1 67 corr
m∠b = 132
m∠rst _

Explanation:

First Figure:

Step1: Identify the relationship

The angle of \(67^{\circ}\) and \(\angle1\) are corresponding angles.

Step2: Use the Corresponding Angles Postulate

Since the lines are parallel and cut by a transversal, corresponding angles are equal. So \(m\angle1 = 67^{\circ}\).

Second Figure:

Step1: Identify the relationship

The angle of \(48^{\circ}\) and \(\angle b\) are consecutive interior angles.

Step2: Use the Consecutive Interior Angles Theorem

Consecutive interior angles are supplementary (\(m\angle b+48^{\circ}=180^{\circ}\)).

Step3: Solve for \(m\angle b\)

\(m\angle b=180^{\circ}- 48^{\circ}=132^{\circ}\)

Third Figure:

Step1: Identify the relationship

The \(138^{\circ}\) angle and \(\angle RST\) are supplementary (they form a linear - pair).

Step2: Use the linear - pair property

\(m\angle RST + 138^{\circ}=180^{\circ}\)

Step3: Solve for \(m\angle RST\)

\(m\angle RST=180^{\circ}-138^{\circ}=42^{\circ}\)

Answer:

\(m\angle1 = 67^{\circ}\), \(m\angle b = 132^{\circ}\), \(m\angle RST=42^{\circ}\)