I will solve this problem by analyzing each of the 9 figures to find the value of $x$ where two parallel lines are cut by a transversal. I'll use the properties of corresponding angles, alternate interior angles, and supplementary angles.
Let me go through each figure one by one:
Figure 1:
- We have two parallel lines cut by a transversal.
- The angle marked 146° and the angle marked 34° are on the same side of the transversal but on different parallel lines.
- The angle marked $x$ is vertically opposite to the 34° angle.
- Vertically opposite angles are equal, so $x = 34°$.
Figure 2:
- Two parallel lines cut by a transversal.
- The angle marked 93° and the angle marked 87° are on the same side of the transversal.
- The angle marked $x$ is corresponding to the 93° angle.
- Corresponding angles are equal when two parallel lines are cut by a transversal, so $x = 93°$.
Figure 3:
- Two parallel lines cut by a transversal.
- The angle marked 75° and the angle marked 105° are on the same side of the transversal.
- The angle marked $x$ is corresponding to the 105° angle.
- Corresponding angles are equal, so $x = 105°$.
Figure 4:
- Two parallel lines cut by a transversal.
- The angle marked 69° and the angle marked 111° are on the same side of the transversal.
- The angle marked $x$ is corresponding to the 69° angle.
- Corresponding angles are equal, so $x = 69°$.
Figure 5:
- Two parallel lines cut by a transversal.
- The angle marked 150° and the angle marked 30° are on the same side of the transversal.
- The angle marked $x$ is corresponding to the 30° angle.
- Corresponding angles are equal, so $x = 30°$.
Figure 6:
- Two parallel lines cut by a transversal.
- The angle marked 28° and the angle marked 52° are on the same side of the transversal.
- The angle marked $x$ is corresponding to the 52° angle.
- Corresponding angles are equal, so $x = 52°$.
Figure 7:
- Two parallel lines cut by a transversal.
- The angle marked 131° and the angle marked 49° are on the same side of the transversal.
- The angle marked $x$ is corresponding to the 49° angle.
- Corresponding angles are equal, so $x = 49°$.
Figure 8:
- Two parallel lines cut by a transversal.
- The angle marked 103° and the angle marked 77° are on the same side of the transversal.
- The angle marked $x$ is corresponding to the 77° angle.
- Corresponding angles are equal, so $x = 77°$.
Figure 9:
- Two parallel lines cut by a transversal.
- The angle marked 114° and the angle marked 66° are on the same side of the transversal.
- The angle marked $x$ is corresponding to the 66° angle.
- Corresponding angles are equal, so $x = 66°$.
Therefore, the values of $x$ for each figure are:
1) $x = 34°$
2) $x = 93°$
3) $x = 105°$
4) $x = 69°$
5) $x = 30°$
6) $x = 52°$
7) $x = 49°$
8) $x = 77°$
9) $x = 66°$
Parent Tip: Review the logic above to help your child master the concept of geometry lines and angles worksheet.
