1.According to the diagrams, find the unknown angles and fill in the table.

The problem asks to find the unknown angles in right-angled triangles and fill in a table. Right-angled triangles have one angle equal to 90 degrees. The sum of angles in any triangle is 180 degrees. Therefore, in a right-angled triangle, the sum of the two acute angles is 180 - 90 = 90 degrees. Let's analyze each diagram and row in the table: * Figure 1: This triangle has an angle of 30 degrees labeled as angle B. It is a right-angled triangle, meaning angle C is 90 degrees. We need to find angle A. Angle A = 180° - 90° - 30° = 60°. The table row corresponds to angle B = 30°. * Figure 2: This triangle has an angle of 25 degrees labeled as angle A. It is a right-angled triangle, meaning angle C is 90 degrees. We need to find angle B. Angle B = 180° - 90° - 25° = 65°. The table row corresponds to angle A = 25°. * Figure 3: This triangle has an angle of 50 degrees labeled as angle A. It is a right-angled triangle, meaning angle C is 90 degrees. We need to find angle B. Angle B = 180° - 90° - 50° = 40°. The table row corresponds to angle A = 50°. * Figure 4: This triangle has an angle of 45 degrees labeled as angle B. It is a right-angled triangle, meaning angle C is 90 degrees. We need to find angle A. Angle A = 180° - 90° - 45° = 45°. The table row corresponds to angle B = 45°. Now, let's fill the table based on the figures and the calculations: | № | ∠C | ∠A | ∠B | ∠A + ∠B | |---|----|----|----|-----------| | 1 | 90°| 60°| 30°| 90° | | 2 | 90°| 65°| 25°| 90° | | 3 | 90°| 25°| 65°| 90° | | 4 | 90°| 45°| 45°| 90° | *Note: The figures provided in the problem description might not be perfectly to scale, and some labels in the table seem to refer to angles from different figures than the ones directly adjacent to the table row. Based on the context of finding unknown angles in right triangles and the typical structure of such problems, we are inferring the connections. However, if we strictly follow the visual placement where row 1 is associated with 'рис.1', row 2 with 'рис.2' (which has 25 degrees at A), and row 3 with another triangle where 25 degrees is at A (implied), and row 4 with an angle of 45 degrees at B, the following interpretation is made for the table completion. Let's re-evaluate based on the visual cues more directly connecting table rows to the figures and explicitly labeled angles: * Figure 1 (рис.1): Appears in row 1. Angle B = 30°. This is a right-angled triangle, so ∠C = 90°. Then ∠A = 180° - 90° - 30° = 60°. * Figure 2 (рис.2): Appears in row 3. Angle A = 25°. This is a right-angled triangle, so ∠C = 90°. Then ∠B = 180° - 90° - 25° = 65°. * Figure 3 (рис.3): Appears in row 2 (implied connection by angle value). Angle A = 50°. This is a right-angled triangle, so ∠C = 90°. Then ∠B = 180° - 90° - 50° = 40°. * Figure 4 (рис.4): Appears in row 4. Angle B = 45°. This is a right-angled triangle, so ∠C = 90°. Then ∠A = 180° - 90° - 45° = 45°. Filling the table with these assignments: | № | ∠C | ∠A | ∠B | ∠A + ∠B | |---|----|----|----|-----------| | 1 | 90°| 60°| 30°| 90° | | 2 | 90°| 40°| 50°| 90° | | 3 | 90°| 25°| 65°| 90° | | 4 | 90°| 45°| 45°| 90° | This interpretation assumes the angles listed in the table (30°, 50°, 25°, 45°) are the known acute angles, and we need to find the other acute angle and then fill the table. The arrows in the table likely indicate that the value in that column (e.g., 30° in row 1 under ∠B) is given, and the arrow points to the column for the angle to be calculated (∠A). For row 1, given ∠B=30°, we calculate ∠A=60°. For row 2, given ∠B=50°, we calculate ∠A=40°. For row 3, given ∠A=25°, we calculate ∠B=65°. For row 4, given ∠B=45°, we calculate ∠A=45°. The table seems to be asking to fill in the *other* acute angle when one is given. The arrows indicate which angle is given. * Row 1: Given ∠B = 30°. ∠A is unknown. In a right triangle, ∠A + ∠B = 90°. So, ∠A = 90° - 30° = 60°. * Row 2: Given ∠B = 50°. ∠A is unknown. ∠A = 90° - 50° = 40°. * Row 3: Given ∠A = 25°. ∠B is unknown. ∠B = 90° - 25° = 65°. * Row 4: Given ∠B = 45°. ∠A is unknown. ∠A = 90° - 45° = 45°. Also, for all rows, ∠C is 90° as they are right-angled triangles. Let's fill the table according to this interpretation: 2. Make a conclusion about the sum of acute angles in a right-angled triangle. Based on the completed table, we can see that in each row, the sum of the two acute angles (∠A + ∠B) is 90°. This is a fundamental property of right-angled triangles: the two acute angles are complementary, meaning they add up to 90 degrees. Conclusion: The sum of the acute angles in a right-angled triangle is always 90 degrees.