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To solve this problem, we need to identify which triangle is similar to \(\Delta PQR\), where \(\angle P = 55^\circ\) and \(\angle Q = 100^\circ\). Two triangles are similar if their corresponding angles are equal.

First, let's find the third angle in \(\Delta PQR\):
\[
\text{Sum of angles in a triangle} = 180^\circ
\]
\[
\angle R = 180^\circ - \angle P - \angle Q = 180^\circ - 55^\circ - 100^\circ = 25^\circ
\]
So, \(\Delta PQR\) has the angles:
\[
\angle P = 55^\circ, \quad \angle Q = 100^\circ, \quad \angle R = 25^\circ
\]

Now, let's examine the triangles:

- **A**: The angles are \(55^\circ\) and \(45^\circ\). The third angle would be \(180^\circ - 55^\circ - 45^\circ = 80^\circ\). This does not match \(\Delta PQR\), so triangle A is not similar.
- **B**: The angles are \(55^\circ\), \(90^\circ\) (right angle). The third angle would be \(180^\circ - 55^\circ - 90^\circ = 35^\circ\). This does not match \(\Delta PQR\), so triangle B is not similar.
- **C**: The angles are \(55^\circ\) and \(65^\circ\). The third angle would be \(180^\circ - 55^\circ - 65^\circ = 60^\circ\). This does not match \(\Delta PQR\), so triangle C is not similar.
- **D**: The angles are \(55^\circ\) and \(25^\circ\). The third angle would be \(180^\circ - 55^\circ - 25^\circ = 100^\circ\). This matches \(\Delta PQR\), so triangle D is similar.

Thus, the correct answer is **D**.

Would you like further details or have any questions?

Here are five related questions to deepen your understanding:
1. What are the properties of similar triangles?
2. How do you calculate the missing angle in any triangle?
3. What is the difference between similar and congruent triangles?
4. How can the angle sum property of a triangle be used in other geometric problems?
5. Can triangles be similar if none of their angles match exactly?

**Tip**: Always remember the sum of the interior angles of any triangle is \(180^\circ\). This rule helps in checking for similarity in triangles!

In ∆PQR, ∠P = 55° and ∠Q = 100°. Which of the following triangles is similar to ∆PQR?

Explore how to determine which triangle is similar to ∆PQR given angles 55° and 100°. This problem utilizes the angle sum property and teaches you to match angles for triangle similarity. Suitable for students in Grades 8-10.

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