To find the measure of angle $A$ in this isosceles triangle, let's analyze the information provided in the diagram.

Step 1: Identify Given Angles and Relationships

1. We have one angle labeled as $112^\circ$.
2. Another angle is labeled $x^\circ$.
3. The third angle is labeled $(2x)^\circ$.
4. The markings on the sides indicate that this is an isosceles triangle, so two angles will be equal.

Step 2: Set Up the Equation for the Triangle’s Interior Angles

In any triangle, the sum of the interior angles is $180^\circ$. So we can write: $112^\circ + x + 2x = 180^\circ$

Step 3: Simplify the Equation

Combine like terms: $112^\circ + 3x = 180^\circ$

Step 4: Solve for $x$

1. Subtract $112^\circ$ from both sides: $3x = 68^\circ$
2. Divide by 3: $x = 22.67^\circ$

Step 5: Calculate Angle $A$

Angle $A$ is given as $2x$, so substitute $x = 22.67^\circ$: $A = 2 \times 22.67^\circ = 45.34^\circ$

Therefore, the measure of angle $A$ is approximately $45.34^\circ$.

Would you like more details on any part of this solution, or do you have additional questions?

Here are five questions that expand on this information:

1. How do we determine when a triangle is isosceles based on side markings?
2. Why do the angles of any triangle sum to 180 degrees?
3. How does identifying equal angles in isosceles triangles simplify angle calculations?
4. What other methods could solve for unknown angles in a triangle?
5. How does solving for variables in geometric problems differ from algebraic problems?

Tip: In an isosceles triangle, if two sides are marked as equal, the angles opposite those sides are also equal. This can help simplify finding unknown angles.