Geometry Unit 3 Angle Pairs Addition Bisectors Worksheet - Free Printable

To solve the problems in the worksheet, we need to use the properties of angles formed by parallel lines and transversals. Here are the key concepts:

1. Corresponding Angles: When two parallel lines are cut by a transversal, corresponding angles are equal.
2. Alternate Interior Angles: When two parallel lines are cut by a transversal, alternate interior angles are equal.
3. Same-Side Interior Angles: When two parallel lines are cut by a transversal, same-side interior angles are supplementary (sum to 180°).
4. Vertical Angles: Vertical angles are always equal.
5. Supplementary Angles: Two angles that add up to 180° are supplementary.

Let's solve each problem step by step.

---

Problem 1: \( x = 180^\circ - 130^\circ \)

- The angle given is \( 130^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 130^\circ = 50^\circ
\]
- Answer: \( x = 50^\circ \)

---

Problem 2: \( x = 180^\circ - 70^\circ \)

- The angle given is \( 70^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 70^\circ = 110^\circ
\]
- Answer: \( x = 110^\circ \)

---

Problem 3: \( x = 180^\circ - 110^\circ \)

- The angle given is \( 110^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 110^\circ = 70^\circ
\]
- Answer: \( x = 70^\circ \)

---

Problem 4: \( x = 180^\circ - 160^\circ \)

- The angle given is \( 160^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 160^\circ = 20^\circ
\]
- Answer: \( x = 20^\circ \)

---

Problem 5: \( x = 180^\circ - 140^\circ \)

- The angle given is \( 140^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 140^\circ = 40^\circ
\]
- Answer: \( x = 40^\circ \)

---

Problem 6: \( x = 180^\circ - 120^\circ \)

- The angle given is \( 120^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 120^\circ = 60^\circ
\]
- Answer: \( x = 60^\circ \)

---

Problem 7: \( x = 90^\circ - 30^\circ \)

- The triangle is a right triangle, and one of the angles is \( 30^\circ \).
- The sum of angles in a triangle is \( 180^\circ \), and one angle is \( 90^\circ \). Therefore:
\[
x = 180^\circ - 90^\circ - 30^\circ = 60^\circ
\]
- Answer: \( x = 60^\circ \)

---

Problem 8: \( x = 180^\circ - 110^\circ \)

- The angle given is \( 110^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 110^\circ = 70^\circ
\]
- Answer: \( x = 70^\circ \)

---

Problem 9: \( x = 180^\circ - 130^\circ \)

- The angle given is \( 130^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 130^\circ = 50^\circ
\]
- Answer: \( x = 50^\circ \)

---

Problem 10: \( x = 180^\circ - 140^\circ \)

- The angle given is \( 140^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 140^\circ = 40^\circ
\]
- Answer: \( x = 40^\circ \)

---

Problem 11: \( x = 180^\circ - 120^\circ \)

- The angle given is \( 120^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 120^\circ = 60^\circ
\]
- Answer: \( x = 60^\circ \)

---

Problem 12: \( x = 180^\circ - 110^\circ \)

- The angle given is \( 110^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 110^\circ = 70^\circ
\]
- Answer: \( x = 70^\circ \)

---

Problem 13: \( x = 180^\circ - 130^\circ \)

- The angle given is \( 130^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 130^\circ = 50^\circ
\]
- Answer: \( x = 50^\circ \)

---

Problem 14: \( x = 180^\circ - 140^\circ \)

- The angle given is \( 140^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 140^\circ = 40^\circ
\]
- Answer: \( x = 40^\circ \)

---

Problem 15: \( x = 180^\circ - 120^\circ \)

- The angle given is \( 120^\circ \), and it is part of a linear pair with \( x \).
- Linear pairs are supplementary, so:
\[
x = 180^\circ - 120^\circ = 60^\circ
\]
- Answer: \( x = 60^\circ \)

---

Final Answer:

\[
\boxed{50, 110, 70, 20, 40, 60, 60, 70, 50, 40, 60, 70, 50, 40, 60}
\]