Find $m\angle ABD$ and $m\angle CBD$   given   $m\angle ABC\ =\ 77\degree$ .

We are given that $ m\angle ABC = 77^\circ $, and we are tasked with finding $ m\angle ABD $ and $ m\angle CBD $. To solve this, we need additional details about the relationship between points $ A $, $ B $, $ C $, and $ D $, such as whether $ D $ is a point on $ \overrightarrow{BC} $, or if there is some angle-splitting taking place. 

Typically, in these types of problems, $ \angle ABC $ is split into $ \angle ABD $ and $ \angle CBD $, and we assume that:

\[
m\angle ABC = m\angle ABD + m\angle CBD
\]

But without further information, we can't split $ \angle ABC $ into $ \angle ABD $ and $ \angle CBD $ in a specific ratio or amount.

Could you provide additional details, such as the position of point $ D $ or how the angles are related?

### 5 Related Questions:
1. If $ \angle ABD = \angle CBD $, what would their measures be?
2. How would the result change if $ D $ is on the angle bisector of $ \angle ABC $?
3. What if $ D $ is outside triangle $ ABC $? How would that affect the angle measures?
4. Can we apply any known theorems (e.g., Angle Bisector Theorem) to this problem?
5. What happens to the angles if a triangle is formed with points $ A $, $ B $, and $ C $?

### Tip:
Always try to visualize geometric problems with a diagram to better understand the relationships between the points and angles.

Find $m\angle ABD$ and $m\angle CBD$ given $m\angle ABC = 77^\circ$.

Learn how to find the measures of angles ABD and CBD when m\angle ABC = 77°. This geometry problem covers angle relationships and the angle sum property, suitable for students in Grades 8-10.

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