Answer:
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°
