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The problem provides two triangles, \( \triangle MNO \) and \( \triangle PQR \), which are similar. This means corresponding angles of the triangles are congruent. 

- \( \angle M = \angle P = 84^\circ \) (given in the diagram).
- \( \angle R = 55.5^\circ \) (given in the diagram), so \( \angle N \) corresponds to \( \angle R \).

To find the measure of \( \angle N \), we can use the fact that the sum of angles in a triangle is always \( 180^\circ \).

\[
\angle N = 180^\circ - (\angle M + \angle O)
\]

From the equation provided, this will be:

\[
\angle N = 180^\circ - (84^\circ + 55.5^\circ)
\]

Now let's compute the value:

\[
\angle N = 180^\circ - 139.5^\circ = 40.5^\circ
\]

Thus, the measure of \( \angle N \) is \( 40.5^\circ \).

Would you like more details on any step?

Here are 5 related questions:
1. How do you identify corresponding angles in similar triangles?
2. What properties of similar triangles are useful in geometry problems?
3. How would the approach differ if the triangles were not similar?
4. Can you apply this concept to find missing side lengths in similar triangles?
5. What is the importance of knowing the sum of angles in any triangle?

**Tip:** Always remember that the sum of the interior angles of any triangle is \( 180^\circ \).

In the figure below, triangle MNO is similar to triangle PQR. What is the measure of angle N? Complete the equation to show how to find the measure of angle N.

Learn how to find the missing angle in similar triangles using the angle sum theorem. This problem focuses on triangles MNO and PQR, and demonstrates how corresponding angles in similar triangles are congruent. Suitable for students in Grades 7-10.

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