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.