We are given a triangular lot with three angles: $A$, $B$, and $C$. The sum of the angles in any triangle is always 180°. Therefore, the relationship between the angles in triangle ABC can be written as:

$A + B + C = 180^\circ$

Given ranges:

• Angle $A$ ranges from $55^\circ$ to $65^\circ$, i.e., $55^\circ \leq A \leq 65^\circ$
• Angle $C$ ranges from $100^\circ$ to $110^\circ$, i.e., $100^\circ \leq C \leq 110^\circ$

Finding the range for angle $B$:

To determine the range for angle $B$, we can subtract the sum of angles $A$ and $C$ from 180°:

$B = 180^\circ - A - C$

1. When $A$ is at its minimum (55°) and $C$ is at its maximum (110°): $B = 180^\circ - 55^\circ - 110^\circ = 15^\circ$

2. When $A$ is at its maximum (65°) and $C$ is at its minimum (100°): $B = 180^\circ - 65^\circ - 100^\circ = 15^\circ$

3. When $A$ is at its maximum (65°) and $C$ is at its maximum (110°): $B = 180^\circ - 65^\circ - 110^\circ = 5^\circ$

4. When $A$ is at its minimum (55°) and $C$ is at its minimum (100°): $B = 180^\circ - 55^\circ - 100^\circ = 25^\circ$

From these calculations, we can see that the range for angle $B$ is:

$5^\circ \leq B \leq 25^\circ$

Final Answer:

The range of angle $B$ is from $5^\circ$ to $25^\circ$.

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Would you like more details on any of the steps? Here are some related questions for further exploration:

1. How do you calculate the angles in a triangle if one angle is given?
2. Can the angles of a triangle ever exceed 180°?
3. What happens if the angles do not sum to 180°?
4. How do we find the missing angles in non-right triangles?
5. What is the significance of angle ranges in geometry?

Tip: Always check the sum of angles in any triangle. If they don't add to 180°, there's likely a mistake in the problem or assumptions.