https://file.aiquickdraw.com/mathbot/file/1726578760946l38crc2r.jpg

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 \( 90^\circ \).

Solve for m∠ABD in the given geometric diagram.

Learn how to solve for angle ABD using the supplementary angles concept. This problem involves identifying angle relationships and applying the formula m∠ABD + m∠ABC = 180°. Suitable for students in Grades 8-10.

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