Question

pg. 75-76 # 5-11 odds (from the notes), 15, 17-20, 21,22

1. generalize in the diagram shown, if x + y = 180, label the remaining angles as x° or y°.

identify a pair of angles for each type. see example 1

1. same - side interior
2. corresponding
3. alternate exterior
4. which angles are supplementary to ∠1? which are congruent to ∠1? see example 2

Explanation:

Step1: Recall angle - pair definitions

Same - side interior angles are two angles that lie between two lines and on the same side of a transversal. Corresponding angles are in the same relative position with respect to the lines and the transversal. Alternate exterior angles are two angles that lie outside the two lines and on opposite sides of the transversal. Supplementary angles add up to 180 degrees and congruent angles have the same measure.

Step2: Identify same - side interior angles

For question 17, a pair of same - side interior angles in the second diagram is $\angle2$ and $\angle5$.

Step3: Identify corresponding angles

For question 18, a pair of corresponding angles in the second diagram is $\angle1$ and $\angle5$.

Step4: Identify alternate exterior angles

For question 19, a pair of alternate exterior angles in the second diagram is $\angle3$ and $\angle6$.

Step5: Find supplementary and congruent angles

For question 20, the angles supplementary to $\angle1$ are $\angle2$, $\angle3$, $\angle6$, $\angle7$. The angles congruent to $\angle1$ are $\angle4$, $\angle5$, $\angle8$.

Answer:

1. $\angle2$ and $\angle5$
2. $\angle1$ and $\angle5$
3. $\angle3$ and $\angle6$
4. Supplementary to $\angle1$: $\angle2$, $\angle3$, $\angle6$, $\angle7$; Congruent to $\angle1$: $\angle4$, $\angle5$, $\angle8$