Linear Pair Angles Lesson Plans & Worksheets Reviewed by Teachers - Free Printable

The image you uploaded is a worksheet titled "Linear Pair Worksheet," which involves solving for missing angles using the Linear Pair Theorem. Below, I will explain the solution step by step for each problem.

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Linear Pair Theorem

The Linear Pair Theorem states that if two angles form a linear pair (i.e., they are adjacent and their non-common sides form a straight line), then the sum of their measures is 180°.

Mathematically:
$$
\text{If } \angle A \text{ and } \angle B \text{ form a linear pair, then } \angle A + \angle B = 180^\circ.
$$

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Solutions to Each Problem

#### Problem 1:
- Given: One angle is \(140^\circ\).
- To find: The measure of the other angle in the linear pair.
- Solution:
$$
\text{Let the unknown angle be } x.
$$
Using the Linear Pair Theorem:
$$
x + 140^\circ = 180^\circ.
$$
Solving for \(x\):
$$
x = 180^\circ - 140^\circ = 40^\circ.
$$
Answer: \(40^\circ\).

#### Problem 2:
- Given: One angle is \(75^\circ\).
- To find: The measure of the other angle in the linear pair.
- Solution:
$$
\text{Let the unknown angle be } x.
$$
Using the Linear Pair Theorem:
$$
x + 75^\circ = 180^\circ.
$$
Solving for \(x\):
$$
x = 180^\circ - 75^\circ = 105^\circ.
$$
Answer: \(105^\circ\).

#### Problem 3:
- Given: One angle is \(110^\circ\).
- To find: The measure of the other angle in the linear pair.
- Solution:
$$
\text{Let the unknown angle be } x.
$$
Using the Linear Pair Theorem:
$$
x + 110^\circ = 180^\circ.
$$
Solving for \(x\):
$$
x = 180^\circ - 110^\circ = 70^\circ.
$$
Answer: \(70^\circ\).

#### Problem 4:
- Given: One angle is \(90^\circ\) (a right angle).
- To find: The measure of the other angle in the linear pair.
- Solution:
$$
\text{Let the unknown angle be } x.
$$
Using the Linear Pair Theorem:
$$
x + 90^\circ = 180^\circ.
$$
Solving for \(x\):
$$
x = 180^\circ - 90^\circ = 90^\circ.
$$
Answer: \(90^\circ\).

#### Problem 5:
- Given: One angle is \(125^\circ\).
- To find: The measure of the other angle in the linear pair.
- Solution:
$$
\text{Let the unknown angle be } x.
$$
Using the Linear Pair Theorem:
$$
x + 125^\circ = 180^\circ.
$$
Solving for \(x\):
$$
x = 180^\circ - 125^\circ = 55^\circ.
$$
Answer: \(55^\circ\).

#### Problem 6:
- Given: One angle is \(130^\circ\).
- To find: The measure of the other angle in the linear pair.
- Solution:
$$
\text{Let the unknown angle be } x.
$$
Using the Linear Pair Theorem:
$$
x + 130^\circ = 180^\circ.
$$
Solving for \(x\):
$$
x = 180^\circ - 130^\circ = 50^\circ.
$$
Answer: \(50^\circ\).

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Final Answers

1. \(40^\circ\)
2. \(105^\circ\)
3. \(70^\circ\)
4. \(90^\circ\)
5. \(55^\circ\)
6. \(50^\circ\)

$$
\boxed{40^\circ, 105^\circ, 70^\circ, 90^\circ, 55^\circ, 50^\circ}
$$