Comparison of two triangles with given angles.

Let’s solve this step by step.

We are given two triangles: triangle PQR and triangle XYZ.

In triangle PQR:
- Angle at P = 60°
- Angle at Q = 70°
- We can find angle at R using the fact that the sum of angles in any triangle is 180°.

So, angle R = 180° - (60° + 70°) = 180° - 130° = 50°

Now look at triangle XYZ:
- Angle at X = 60°
- Angle at Z = 50°
- Let’s find angle at Y: 180° - (60° + 50°) = 180° - 110° = 70°

So now we have:

Triangle PQR angles:
P = 60°, Q = 70°, R = 50°

Triangle XYZ angles:
X = 60°, Y = 70°, Z = 50°

That means the angles match exactly — just labeled differently.

So:
- Angle P (60°) matches angle X (60°)
- Angle Q (70°) matches angle Y (70°)
- Angle R (50°) matches angle Z (50°)

Therefore, the triangles are similar because all three corresponding angles are equal.

But the question doesn’t ask for similarity — it just shows the diagrams. Since no specific question was asked in the image, but based on typical problems like this, the most likely task is to find the missing angle or compare the triangles.

Wait — looking again, maybe the problem is to find the missing angle in one of them? But both triangles already have all angles shown or calculable.

Actually, let me recheck: In triangle PQR, angles are 60°, 70°, so third is 50° — which matches angle Z in the other triangle.

In triangle XYZ, angles are 60°, 50°, so third is 70° — which matches angle Q.

So perhaps the problem is to identify which angles correspond?

But since there’s no explicit question, I’ll assume the most common type: “Are these triangles similar?” or “Find the missing angle.”

Since both triangles have angles 50°, 60°, 70°, they are similar.

But if the problem is simply to find the missing angle in each, then:

For triangle PQR: angle R = 50°
For triangle XYZ: angle Y = 70°

But again — no explicit question.

Wait — perhaps the original problem (not fully visible) asks something like “What is the measure of angle R?” or “What is the measure of angle Y?”

Given that, and since in many such problems, they ask for the unknown angle, let’s suppose the task is to find the missing angle in each triangle.

In triangle PQR:
Angles given: 60° and 70° → missing angle R = 180 - 60 - 70 = 50°

In triangle XYZ:
Angles given: 60° and 50° → missing angle Y = 180 - 60 - 50 = 70°

So if the question is “Find the missing angles”, then:

Angle R = 50°
Angle Y = 70°

But since the user didn’t specify the exact question, and based on standard textbook problems with such diagrams, it’s very likely that the problem is to determine whether the triangles are similar, or to find the missing angles.

However, looking at the way the angles are marked, and since both triangles end up having the same set of angles (50°, 60°, 70°), they are similar.

But to be safe, let’s consider: maybe the problem is to find angle R and angle Y?

I think the safest assumption is that the problem is to find the missing angle in each triangle.

So:

In triangle PQR:
Sum of angles = 180°
Given: ∠P = 60°, ∠Q = 70°
∠R = 180° - 60° - 70° = 50°

In triangle XYZ:
Given: ∠X = 60°, ∠Z = 50°
∠Y = 180° - 60° - 50° = 70°

Final Answer:
Angle R = 50°, Angle Y = 70°