Printable geometry worksheet designed for partner work, featuring five problems each for Partner A and Partner B to solve using angle theorems.

Problem Overview:

The task involves solving problems related to the Angle Addition Postulate and the Angle Bisector Theorem. The worksheet is designed for a partner activity, where Partner A and Partner B are working together to solve geometric problems involving angles.

Key Concepts:

1. Angle Addition Postulate: If a point lies in the interior of an angle, then the measure of the whole angle is equal to the sum of the measures of the two smaller angles formed.
- Mathematically: If point \( D \) lies in the interior of \( \angle ABC \), then \( m\angle ABD + m\angle DBC = m\angle ABC \).

2. Angle Bisector Theorem: An angle bisector divides an angle into two congruent angles.
- Mathematically: If \( BD \) bisects \( \angle ABC \), then \( m\angle ABD = m\angle DBC \).

Solution to Each Problem:

#### Problem 1:
- Partner A: \( m\angle 1 = 30^\circ \)
- Partner B: \( m\angle 2 = 60^\circ \)

Using the Angle Addition Postulate:
\[ m\angle 1 + m\angle 2 = m\angle ABC \]
\[ 30^\circ + 60^\circ = 90^\circ \]

So, \( m\angle ABC = 90^\circ \).

#### Problem 2:
- Partner A: \( m\angle 1 = 45^\circ \)
- Partner B: \( m\angle 2 = 45^\circ \)

Using the Angle Addition Postulate:
\[ m\angle 1 + m\angle 2 = m\angle ABC \]
\[ 45^\circ + 45^\circ = 90^\circ \]

So, \( m\angle ABC = 90^\circ \).

#### Problem 3:
- Partner A: \( m\angle 1 = 70^\circ \)
- Partner B: \( m\angle 2 = 20^\circ \)

Using the Angle Addition Postulate:
\[ m\angle 1 + m\angle 2 = m\angle ABC \]
\[ 70^\circ + 20^\circ = 90^\circ \]

So, \( m\angle ABC = 90^\circ \).

#### Problem 4:
- Partner A: \( m\angle 1 = 50^\circ \)
- Partner B: \( m\angle 2 = 50^\circ \)

Using the Angle Addition Postulate:
\[ m\angle 1 + m\angle 2 = m\angle ABC \]
\[ 50^\circ + 50^\circ = 100^\circ \]

So, \( m\angle ABC = 100^\circ \).

#### Problem 5:
- Partner A: \( m\angle 1 = 60^\circ \)
- Partner B: \( m\angle 2 = 30^\circ \)

Using the Angle Addition Postulate:
\[ m\angle 1 + m\angle 2 = m\angle ABC \]
\[ 60^\circ + 30^\circ = 90^\circ \]

So, \( m\angle ABC = 90^\circ \).

Final Answers:

1. \( m\angle ABC = 90^\circ \)
2. \( m\angle ABC = 90^\circ \)
3. \( m\angle ABC = 90^\circ \)
4. \( m\angle ABC = 100^\circ \)
5. \( m\angle ABC = 90^\circ \)

Boxed Final Answer:

\[
\boxed{90^\circ, 90^\circ, 90^\circ, 100^\circ, 90^\circ}
\]