https://file.aiquickdraw.com/mathbot/file/1726827067099dlzss2bc.jpg

In the given diagram, we are tasked with finding the measure of \( \angle ABC \). Here's the breakdown:

We are given:
- \( m \angle ABD = 76^\circ \)
- \( m \angle DBC = 68^\circ \)

Now, \( \angle ABC \) is the sum of \( \angle ABD \) and \( \angle DBC \), because points \( A \), \( B \), \( D \), and \( C \) are arranged in such a way that \( \angle ABC \) consists of the two adjacent angles \( \angle ABD \) and \( \angle DBC \).

Thus:
\[
m \angle ABC = m \angle ABD + m \angle DBC
\]
\[
m \angle ABC = 76^\circ + 68^\circ = 144^\circ
\]

So, the measure of \( \angle ABC = 144^\circ \).

Would you like more details or have any questions?

### Relative Questions:
1. How do you determine if two angles are adjacent?
2. What is the significance of the sum of angles around a point?
3. Can the sum of adjacent angles be more than \(180^\circ\)?
4. How would this change if it were a triangle instead of straight lines?
5. Can the sum of two angles be equal to \(180^\circ\) in all cases?

### Tip:
Always ensure that the angles you are working with are correctly identified as adjacent or supplementary, as this can affect your calculations.

If m∠ABD = 76°, and m∠DBC = 68°, then m∠ABC = [?]°

Learn how to calculate the measure of angle ABC when given adjacent angles ABD and DBC. In this problem, we use the Angle Addition Postulate to find the solution. Suitable for students in Grades 6-8.

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