# Determining Angle Measure With Parallel Lines Worksheets With Answer Key - Johnny Wolfe, Jay High School Santa Rosa County Florida - 2001

Determining Angle Measure with Parallel Lines Examples
1. Using the figure at the right, review with students
the following angles: corresponding, alternate
interior, alternate exterior and consecutive interior.
Corresponding Angles
∠ 1 and ∠ 5,
∠ 3 and ∠ 7,
∠ 2 and ∠ 6,
∠ 4 and ∠ 8
Alternate Interior Angles
∠ 3 and ∠ 6,
∠ 4 and ∠ 5
Alternate Exterior Angles
Consecutive Interior Angles
∠ 1 and ∠ 8,
∠ 2 and ∠ 7
∠ 3 and ∠ 5,
∠ 4 and ∠ 6
2. There are several postulates and theorems that help you gain insight into
properties of parallel lines. If you investigate the relationships between the
corresponding angles formed by two parallel lines cut by a transversal, you will
observe that the angles are congruent. This property is accepted as a postulate.
3. Corresponding Angles Postulate – If two parallel lines are cut by a transversal,
then each pair of corresponding angles is congruent.
This postulate, combined with linear pair and vertical angle
properties, helps to establish several angle relationships.
4. Example – A road crosses a set of railroad tracks. If the
measure of ∠ 6 is 110
, find m ∠ 3.
o
Since ∠ 2 and ∠ 6 are corresponding angles, m ∠ 2 = m ∠ 6,
m ∠ 2 =m ∠ 3 because they are vertical angles. Therefore,
m ∠ 6 = m ∠ 3 by the transitive property of equality. So,
m ∠ 3 = 110
o
.
Johnny Wolfe Determining Angle Measure with Parallel Lines
Jay High School
Santa Rosa
County Florida
September 14, 2001