To solve this problem, let's consider the properties of angles formed when two lines intersect.

When two lines intersect, they form two pairs of opposite (or vertical) angles. These vertical angles are always equal.

Given in the diagram:

• One angle is $110^\circ$.
• The opposite angle is labeled as $(10x + 10)^\circ$.

Since these are vertical angles, they must be equal. Therefore, we can set up the equation:

$(10x + 10)^\circ = 110^\circ$

This matches Choice A.

Correct Answer:

• (Choice A) $(10x + 10) = 110$

Would you like further details or have any questions?

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Here are 5 related questions:

1. What are vertical angles and why are they always equal?
2. How do you solve the equation $(10x + 10) = 110$ for $x$?
3. What other properties of angles are formed when two lines intersect?
4. How can you verify the solution for $x$ once it’s found?
5. What are supplementary angles and how are they different from vertical angles?

Tip: Remember that when two lines intersect, vertical angles are always equal. This property can help solve many geometric problems involving angles.