Answer:
To write an inequality describing the range of x for each pair of triangles, we need to consider the given angles and their relationships. Let's analyze the given information step by step:
1. Triangle XLM:
- Angle LKM = 75°
- Angle LKX = (4x - 29)°
- Angle MKX = (2x + 4)°
Since the sum of the angles in a triangle is always 180°, we can write the following inequality:
(4x - 29) + (2x + 4) + 75 < 180
Simplifying the equation, we get:
6x + 50 < 180
Subtracting 50 from both sides:
6x < 130
Dividing both sides by 6:
x < 21.67
Therefore, the range of x for triangle XLM is x < 21.67.
2. Triangle PNC:
- Angle PNF = 31°
- Angle NPF = 33°
- Angle NCP = (2x + 4)°
Using the same reasoning as before, we can write the following inequality:
31 + 33 + (2x + 4) < 180
Simplifying the equation, we get:
2x + 68 < 180
Subtracting 68 from both sides:
2x < 112
Dividing both sides by 2:
x < 56
Therefore, the range of x for triangle PNC is x < 56.
In summary:
- For triangle XLM, the range of x is x < 21.67.
- For triangle PNC, the range of x is x < 56.
Explanation: