Question

name: interior angles find the value of each indicated angle. 1) 2) 3) 4) 5) 6) 8) alternate are congruent same - side are supplementary (=180) linear pair supplementary (=180)

Explanation:

Step1: Use corresponding - angles property

For parallel lines, corresponding angles are equal. In the first figure, the angle of $65^{\circ}$ and $x$ are corresponding angles. So $x = 65^{\circ}$.

Step2: Use linear - pair property

In the second figure, the angle of $114^{\circ}$ and $x$ form a linear - pair. Since the sum of angles in a linear - pair is $180^{\circ}$, we have $x=180 - 114=66^{\circ}$.

Step3: Use corresponding - angles property

In the third figure, the angle of $74^{\circ}$ and $x$ are corresponding angles. So $x = 74^{\circ}$.

Step4: Use same - side interior angles property

In the fourth figure, the angle of $120^{\circ}$ and $x$ are same - side interior angles. Since same - side interior angles of parallel lines are supplementary ($180^{\circ}$), we have $x = 180-120 = 60^{\circ}$.

Step5: Use corresponding - angles property

In the fifth figure, the angle of $55^{\circ}$ and $x$ are corresponding angles. So $x = 55^{\circ}$.

Step6: Use corresponding - angles property

In the sixth figure, the angle of $71^{\circ}$ and $x$ are corresponding angles. So $x = 71^{\circ}$.

Step7: Use corresponding - angles property

In the seventh figure, the angle of $149^{\circ}$ and $x$ are corresponding angles. So $x = 149^{\circ}$.

Step8: Use corresponding - angles property

In the eighth figure, the angle of $40^{\circ}$ and $x$ are corresponding angles. So $x = 40^{\circ}$.

Answer:

1. $x = 65^{\circ}$
2. $x = 66^{\circ}$
3. $x = 74^{\circ}$
4. $x = 60^{\circ}$
5. $x = 55^{\circ}$
6. $x = 71^{\circ}$
7. $x = 149^{\circ}$
8. $x = 40^{\circ}$