3. Suppose that MAP and MAC are linear pairs, m ZMAP = 7x - 13 and

mZMAC = 3x + 13.

Part A: Identify the line and the rays that form 2MAP and MAC.

Part B: Determine m MAP.

Part C: Determine mZMAC.

Part A: The line PC and the ray AM formed ∠MAP and ∠MAC

Part B: m∠MAP = 113°

Part C: m∠MAC = 67°

Step-by-step explanation:

* Lets explain what is the linear pairs

- A linear pair of angles is formed when two lines intersect.

- Two angles are said to be linear if they are adjacent angles formed by

two intersecting lines.

- The measure of a straight angle is 180°, so a linear pair of angles

must add up to 180°

* Lets solve the problem

- ∠MAP and ∠MAC are linear pairs

- m∠MAP = 7x - 13

- m∠MAC = 3x + 13

# Part A:

∵ The rays of ∠MAP are AM and AP

∵ The rays of ∠MAC are AM and AC

∴ The common Vertex is A and the common ray is AM

∴ The line is PC and the ray is AM

* The line PC and the ray AM formed ∠MAP and ∠MAC

# Part B:

∵ The measure of linear pairs is 180°

∵ ∠MAP and ∠MAC are linear pairs

∴ m∠MAP + m∠MAC = 180°

∵ m∠MAP = 7x - 13

∵ m∠MAC = 3x + 13

- Substitute these values in the equation above

∴ 7x - 13 + 3x + 13 = 180

∴ 10x = 180

- Divide both sides by 10

∴ x = 18

- To find m∠ MAP substitute the value of x in its expression

∵ m∠MAP = 7x - 13

∵ x = 18

∴ m∠MAP = 7 (18) - 13 = 126 - 13 = 113

* m∠MAP = 113°

# Part C:

- To find m∠ MAC substitute the value of x in its expression

∵ m∠MAP = 3x + 13

∵ x = 18

∴ m∠MAC = 3 (18) + 13 = 54 + 13 = 67

* m∠MAC = 67°