Of course! Let’s solve each problem step by step. The worksheet is titled “Interior Angles,” and all problems involve
parallel lines cut by a transversal. We’ll use key angle relationships:
-
Corresponding angles are equal.
-
Alternate interior angles are equal.
-
Consecutive interior angles (same-side interior) are supplementary (add to 180°).
-
Vertical angles are equal.
-
Linear pairs add to 180°.
---
Problem 1:
Given: A transversal cuts two parallel lines. One angle is 65°, and we need to find the value of
x, which is an
alternate interior angle to the 65° angle.
✔ Solution: Alternate interior angles are equal.
>
x = 65°
---
Problem 2:
Two lines intersect (not necessarily parallel), forming vertical angles. One angle is 134°, and
x is its
vertical angle.
✔ Solution: Vertical angles are equal.
>
x = 134°
*(Note: Even though the lines aren’t labeled as parallel, vertical angles are always equal regardless.)*
---
Problem 3:
Two parallel lines cut by a transversal. One angle is 47°, and
x is on the same side of the transversal, inside the parallel lines — so it’s a
consecutive interior angle (same-side interior).
✔ Solution: Consecutive interior angles are supplementary.
> x + 47° = 180°
>
x = 180° - 47° = 133°
---
Problem 4:
Parallel lines cut by a transversal. One angle is 109°, and
x is its
corresponding angle.
✔ Solution: Corresponding angles are equal.
>
x = 109°
---
Problem 5:
Two lines intersect, forming vertical angles. One angle is 58°, and
x is its
vertical angle.
✔ Solution: Vertical angles are equal.
>
x = 58°
---
Problem 6:
Parallel lines cut by a transversal. One angle is 57°, and
x is its
alternate interior angle.
✔ Solution: Alternate interior angles are equal.
>
x = 57°
---
Problem 7:
Parallel lines cut by a transversal. One angle is 106°, and
x is its
consecutive interior angle (same-side interior).
✔ Solution: Consecutive interior angles are supplementary.
> x + 106° = 180°
>
x = 180° - 106° = 74°
---
Problem 8:
Two lines intersect, forming vertical angles. One angle is 120°, and
x is its
vertical angle.
✔ Solution: Vertical angles are equal.
>
x = 120°
---
##
✔ Final Answers:
1.
x = 65°
2.
x = 134°
3.
x = 133°
4.
x = 109°
5.
x = 58°
6.
x = 57°
7.
x = 74°
8.
x = 120°
Let me know if you’d like a diagram explanation for any of these!
Parent Tip: Review the logic above to help your child master the concept of two parallel lines cut by a transversal worksheet.
