Similar Triangles- Formula, Theorem & Proof of SSS, SAS AAA Similarity - Free Printable

Explanation:
We are given two triangles: △PQR and △XYZ.
In △PQR:
- ∠P = 60°
- ∠Q = 70°
We can find ∠R using the triangle angle sum rule:
Sum of angles in any triangle = 180°
So, ∠R = 180° − ∠P − ∠Q = 180° − 60° − 70° = 50°

In △XYZ:
- ∠X = 60°
- ∠Z = 50°
Then ∠Y = 180° − ∠X − ∠Z = 180° − 60° − 50° = 70°

Now compare the angles:
△PQR: ∠P = 60°, ∠Q = 70°, ∠R = 50°
△XYZ: ∠X = 60°, ∠Y = 70°, ∠Z = 50°

So the corresponding angles match:
∠P ↔ ∠X (60°),
∠Q ↔ ∠Y (70°),
∠R ↔ ∠Z (50°)

That means the triangles are similar by AAA (Angle-Angle-Angle) similarity.

But the question likely asks for a specific value — since no explicit question is written, and only the diagram is provided, the most common task with such a diagram is to find the missing angle in one triangle (often ∠R or ∠Y).

Given that ∠R was not labeled, and we computed it as 50°, and ∠Y was not labeled but computed as 70°, and both triangles have all three angles known now, the most probable expected answer is the measure of ∠R (since it’s the unlabeled angle in the first triangle), which is:

∠R = 50°

Let me double-check:
60 + 70 + 50 = 180 ✔️
60 + 50 + 70 = 180 ✔️

Yes, correct.

Final Answer:
50°