ASSERTION(A):ΔΑΒC = triangle PQR angle A = 30 deg angle B = 80 deg then angle R = 70 deg . REASON (R): The corresponding angles of the congruent triangle are equal.

The assertion (A) and reason (R) provided seem to address the idea of congruent triangles and corresponding angles. Let's analyze both:

### Assertion (A):
The statement "ΔABC = ΔPQR, angle A = 30°, angle B = 80°, then angle R = 70°" implies that the two triangles, ΔABC and ΔPQR, are congruent. If two triangles are congruent, all their corresponding angles and sides are equal.

For ΔABC:
- Angle A = 30°
- Angle B = 80°
  
The sum of angles in a triangle is always 180°. Therefore, angle C in ΔABC can be calculated as:
\[
\text{Angle C} = 180° - 30° - 80° = 70°
\]

Since ΔABC is congruent to ΔPQR, the corresponding angles in ΔPQR must be equal. Hence:
- Angle A corresponds to Angle P, so Angle P = 30°
- Angle B corresponds to Angle Q, so Angle Q = 80°
- Angle C corresponds to Angle R, so Angle R = 70°

Thus, the assertion (A) is correct.

### Reason (R):
"The corresponding angles of the congruent triangles are equal" is the correct reason because, by the definition of congruent triangles, all corresponding angles and sides are equal. Therefore, the reason correctly supports the assertion.

### Conclusion:
- The assertion (A) is **true**.
- The reason (R) is **true**.
- The reason correctly explains the assertion.

Would you like further details or have any questions?

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Here are 5 related questions to consider:

1. How do you determine if two triangles are congruent?
2. What are the different congruence criteria (like SAS, ASA, etc.)?
3. Can triangles with different side lengths have the same corresponding angles?
4. How do you calculate an unknown angle in a triangle given two angles?
5. What is the difference between congruent and similar triangles?

**Tip:** Remember, the sum of the interior angles of any triangle is always 180°.

ASSERTION(A): ΔABC = ΔPQR, angle A = 30°, angle B = 80°, then angle R = 70°. REASON (R): The corresponding angles of the congruent triangle are equal.

Understand how to solve a problem involving congruent triangles ΔABC and ΔPQR, where angle A = 30° and angle B = 80°. Using the angle-sum property and congruence theorem, we calculate angle R = 70°. This problem is suitable for students in Grades 8-10.

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