Question

use the diagram below to answer the following questions. list two pairs of adjacent angles. list two pairs of vertical angles. list two pairs of corresponding angles. list one pair of alternate interior angles. list one pair of same side interior angles. list one pair of alternate exterior angles. list one pair of same side exterior angles.

Explanation:

Step1: Identify adjacent angles

Adjacent angles share a common side and a common vertex. Examples are $\angle1$ and $\angle2$, $\angle3$ and $\angle4$.

Step2: Identify vertical angles

Vertical angles are opposite each other when two lines intersect. Such as $\angle1$ and $\angle3$, $\angle2$ and $\angle4$.

Step3: Identify corresponding angles

Corresponding angles are in the same relative position. For example, $\angle1$ and $\angle5$, $\angle2$ and $\angle6$.

Step4: Identify alternate - interior angles

Alternate - interior angles are between the two lines and on opposite sides of the transversal. Like $\angle2$ and $\angle5$, $\angle3$ and $\angle6$.

Step5: Identify same - side interior angles

Same - side interior angles are between the two lines and on the same side of the transversal. For instance, $\angle2$ and $\angle6$, $\angle3$ and $\angle5$.

Step6: Identify alternate - exterior angles

Alternate - exterior angles are outside the two lines and on opposite sides of the transversal. Such as $\angle1$ and $\angle7$, $\angle4$ and $\angle8$.

Step7: Identify same - side exterior angles

Same - side exterior angles are outside the two lines and on the same side of the transversal. For example, $\angle1$ and $\angle8$, $\angle4$ and $\angle7$.

Answer:

• Two pairs of adjacent angles: $\angle1$ and $\angle2$, $\angle3$ and $\angle4$
• Two pairs of vertical angles: $\angle1$ and $\angle3$, $\angle2$ and $\angle4$
• Two pairs of corresponding angles: $\angle1$ and $\angle5$, $\angle2$ and $\angle6$
• One pair of alternate - interior angles: $\angle2$ and $\angle5$
• One pair of same - side interior angles: $\angle2$ and $\angle6$
• One pair of alternate - exterior angles: $\angle1$ and $\angle7$
• One pair of same - side exterior angles: $\angle1$ and $\angle8$