https://file.aiquickdraw.com/mathbot/file/17303942641146zqb80eb.jpg

To solve this problem, let’s go over the details step-by-step:

1. **Identify the Information Given:**
   - The problem states: "The measure of angle \( A \) is 18 degrees greater than twice the measure of angle \( B \)."
   - We need to determine the measure of angle \( A \).

2. **Define Variables:**
   - Let \( B = x \) (the measure of angle \( B \)).
   - Therefore, the measure of angle \( A \) will be \( 2x + 18 \) (since it is 18 degrees greater than twice angle \( B \)).

3. **Set Up the Equation Using Triangle Sum Property:**
   - In any triangle, the sum of the interior angles is 180 degrees.
   - According to the diagram, we assume it’s a right triangle, meaning one of the angles is 90 degrees.
   - Thus, the equation for the sum of angles becomes:
     \[
     x + (2x + 18) + 90 = 180
     \]

4. **Solve for \( x \):**
   - Combine like terms:
     \[
     3x + 108 = 180
     \]
   - Subtract 108 from both sides:
     \[
     3x = 72
     \]
   - Divide by 3:
     \[
     x = 24
     \]

5. **Determine the Measure of Angle \( A \):**
   - Since \( x = 24 \), angle \( B \) is 24 degrees.
   - Substitute \( x = 24 \) into \( 2x + 18 \) to find angle \( A \):
     \[
     A = 2(24) + 18 = 48 + 18 = 66
     \]

6. **Answer:**
   - The measure of angle \( A \) is 66 degrees.

Would you like further clarification or a breakdown of any specific step?

Here are some related questions to deepen understanding:
1. How would the solution change if angle \( A \) was instead 15 degrees greater than twice angle \( B \)?
2. Can this method be used if angle \( A \) is given in terms of a different relationship with angle \( B \)?
3. What if angle \( A \) was described as three times the measure of angle \( B \) instead of twice?
4. How does the 90-degree angle affect the setup of our equation in this problem?
5. Can you solve for angle \( B \) if angle \( A \) was given as a fixed degree measure instead?

**Tip:** Always remember the Triangle Sum Property: the sum of the angles in any triangle is 180 degrees.

In the accompanying diagram below, the measure of angle A is 18° greater than twice the measure of angle B. Determine the measure of angle A.

Learn how to determine the measure of angle A in a right triangle, where angle A is defined as 18° greater than twice the measure of angle B. This problem covers key concepts including algebra, angle relationships, and the Triangle Sum Property.

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