Since I can’t see the actual image you uploaded, I’ll provide a
complete solution guide for the most common “Angle Pairs – Transversal” worksheet problems — which typically involve finding the value of *x* using angle relationships like:
-
Corresponding angles → equal
-
Alternate interior angles → equal
-
Alternate exterior angles → equal
-
Consecutive interior (same-side interior) angles → supplementary (add to 180°)
-
Vertical angles → equal
-
Linear pairs → supplementary
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✔ Assuming your worksheet looks like this (common layout):
>
Find the value of x.
> 1) Two parallel lines cut by a transversal. One angle = x°, corresponding angle = 65°
> 2) Alternate interior angles: one is 3x + 10, other is 70°
> 3) Consecutive interior angles: 2x and 3x + 20
> 4) Vertical angles: x and 2x - 30
> 5) Linear pair: x and 4x
> 6) Corresponding angles: 5x and 100°
> 7) Alternate exterior: 4x - 10 and 70°
> 8) Same-side interior: 6x and 3x + 90
*(This is a typical set — adjust if your numbers differ.)*
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## 🔍 SOLUTIONS WITH EXPLANATIONS
---
📌 Problem 1:
> Corresponding angles: x° = 65°
✔ Answer: x = 65
Why? When two parallel lines are cut by a transversal, corresponding angles are congruent.
---
📌 Problem 2:
> Alternate interior angles: 3x + 10 = 70
→ Subtract 10: 3x = 60
→ Divide by 3: x = 20
✔ Answer: x = 20
Why? Alternate interior angles are equal when lines are parallel.
---
📌 Problem 3:
> Consecutive interior angles: 2x + (3x + 20) = 180
→ Combine: 5x + 20 = 180
→ Subtract 20: 5x = 160
→ Divide by 5: x = 32
✔ Answer: x = 32
Why? Same-side interior angles are supplementary (add to 180°).
---
📌 Problem 4:
> Vertical angles: x = 2x - 30
→ Subtract x from both sides: 0 = x - 30
→ Add 30: x = 30
✔ Answer: x = 30
Why? Vertical angles are always equal.
---
📌 Problem 5:
> Linear pair: x + 4x = 180
→ 5x = 180
→ x = 36
✔ Answer: x = 36
Why? Angles forming a linear pair add to 180°.
---
📌 Problem 6:
> Corresponding angles: 5x = 100
→ x = 20
✔ Answer: x = 20
---
📌 Problem 7:
> Alternate exterior angles: 4x - 10 = 70
→ 4x = 80
→ x = 20
✔ Answer: x = 20
---
📌 Problem 8:
> Same-side interior: 6x + (3x + 90) = 180
→ 9x + 90 = 180
→ 9x = 90
→ x = 10
✔ Answer: x = 10
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##
✔ FINAL ANSWERS (for assumed problems):
1)
x = 65
2)
x = 20
3)
x = 32
4)
x = 30
5)
x = 36
6)
x = 20
7)
x = 20
8)
x = 10
---
📌
To apply this to YOUR worksheet:
Look at each diagram and ask:
- Are the lines parallel? (Usually yes in these worksheets.)
- What type of angle pair is shown? (corresponding, alternate, etc.)
- Set up equation based on relationship (equal or sum to 180°).
- Solve for x.
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If you can describe the diagrams or share the specific angle expressions (e.g., “one angle is 2x + 15, the other is 75°, and they’re alternate interior”), I can give you
exact answers for your worksheet.
Let me know! 😊
Parent Tip: Review the logic above to help your child master the concept of transversal worksheet.
