Question

use the figure for exercises 1 - 4. identify all pairs of each type of angle.

1. corresponding angles
2. same - side interior angles
3. alternate interior angles
4. alternate exterior angles

use the figure for exercises 5 and 6.

1. which angles are supplementary to the given angle?
2. which angles are congruent to the given angle?
3. complete the two - column proof.

given: ( xparallel y )
prove: ( angle 3congangle 5 )

1. in the figure, ( ehparallel ai ) and ( aiparallel cj ).

a. what is ( mangle 1 )? explain.
b. what is ( mangle 3 )? explain.
envision™ geometry • teaching resources

Explanation:

Step1: Find \(m\angle1\)

Since \(EH\parallel AI\parallel CJ\), and we know that when two parallel lines are cut by a transversal, alternate interior angles are equal. \(\angle1\) and the \(53^{\circ}\) angle are alternate interior angles. So \(m\angle1 = 53^{\circ}\)

Step2: Find \(m\angle3\)

First, we know that \(\angle1\) and \(\angle2\) are complementary (because they form a right - angle at the intersection of the transversals). So \(m\angle2=90^{\circ}-m\angle1\). Substituting \(m\angle1 = 53^{\circ}\), we get \(m\angle2 = 90^{\circ}-53^{\circ}=37^{\circ}\). Then, \(\angle2\) and \(\angle3\) are alternate interior angles (because \(EH\parallel FG\) and the transversal cuts them). So \(m\angle3=m\angle2 = 37^{\circ}\)

Answer:

a. \(m\angle1 = 53^{\circ}\) (alternate interior angles)
b. \(m\angle3 = 37^{\circ}\) (first find \(\angle2 = 90 - 53=37^{\circ}\) using complementary angles, then \(\angle2\) and \(\angle3\) are alternate interior angles)