https://file.aiquickdraw.com/mathbot/file/1730153103072cwm4sm6i.jpg

To solve for \( m \angle 2 \) in this problem, let's go through the information provided:

1. We know:
   \[
   m \angle ABD = 67^\circ
   \]
2. The problem states that:
   \[
   m \angle 1 \text{ is } 5^\circ \text{ more than } m \angle 2
   \]
   
Let’s set \( m \angle 2 = x \). Then, \( m \angle 1 \) would be:
   \[
   m \angle 1 = x + 5
   \]

Since \( \angle 1 \) and \( \angle 2 \) together make up \( \angle ABD \), we can set up the equation:
   \[
   x + (x + 5) = 67
   \]

### Step 1: Solve for \( x \)
\[
2x + 5 = 67
\]
\[
2x = 67 - 5
\]
\[
2x = 62
\]
\[
x = 31
\]

### Step 2: Answer
Thus, \( m \angle 2 = 31^\circ \).

Would you like more details or have any questions?

### Related Questions
1. How would you solve if \( m \angle 1 \) was less than \( m \angle 2 \) by a certain degree?
2. What if \( m \angle ABD \) was given in terms of another angle?
3. How does angle addition work in cases where there are multiple intersecting angles?
4. What if the total angle was not 67° but another value?
5. How can you check the answer to ensure it's accurate?

### Tip
Always write down relationships and equations step-by-step to avoid errors in solving angle problems.

In the figure below, m∠ABD = 67°, and m∠1 is 5° more than m∠2. Find m∠2.

Learn how to determine the measure of angle 2 when given m∠ABD = 67° and that m∠1 is 5° more than m∠2. This solution uses algebraic equations to find angle measures and is suitable for students in Grades 6-8.

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