To solve for $m \angle ABD$, let's analyze the diagram.

From the image, we observe:

• $\angle ABC = 67^\circ$ (shown inside the triangle at $B$).
• The angle on the exterior, $\angle DBC = 126^\circ$, is supplementary to $\angle ABC$ because they form a straight line.

Using the fact that supplementary angles add up to $180^\circ$, we have:

$m \angle ABD + m \angle ABC = 180^\circ$

Substituting $m \angle ABC = 67^\circ$:

$m \angle ABD + 67^\circ = 180^\circ$

Now, solve for $m \angle ABD$:

$m \angle ABD = 180^\circ - 67^\circ = 113^\circ$

Thus, the value of $m \angle ABD$ is $113^\circ$.

Would you like further clarification or additional questions?

Related Questions:

1. How do you calculate supplementary angles in a different context?
2. Can you explain the relationship between complementary and supplementary angles?
3. What is the sum of the interior angles of a triangle, and how can that be applied here?
4. What if you were given two supplementary angles but one in terms of a variable? How would you solve it?
5. How do exterior angles of a polygon relate to interior angles?

Tip:

Remember, supplementary angles always add up to $180^\circ$, while complementary angles sum to $90^\circ$.