All four angles in each rhombus are 45 degrees. This is because opposite angles in a rhombus are equal, and the diagonals bisect each other at right angles.
Rhombus 1:
1. Opposite angles in a rhombus are equal, so angles 1 and 4 are equal, and angles 2 and 3 are equal.
2. The diagonals of a rhombus bisect each other at right angles, so angles 1 and 2 are complementary (add up to 90 degrees).
3. Therefore, angles 1 and 4 are each 45 degrees (half of 90 degrees).
4. The sum of the angles in a quadrilateral is 360 degrees, so angle 1 + angle 2 + angle 3 + angle 4 = 360 degrees.
5. Substituting the values we know, we get 45 degrees + 90 degrees + angle 3 + 45 degrees = 360 degrees.
6. Solving for angle 3, we get angle 3 = 90 degrees.
7. Therefore, all four angles in Rhombus 1 measure 45 degrees.
Rhombus 2:
1. Following the same steps as for Rhombus 1, we can determine that angles 6 and 8 are equal, and angles 7 and 9 are equal.
2. Angles 6 and 7 are complementary, so angles 6 and 8 are each 45 degrees (half of 90 degrees).
3. Angles 7 and 9 are also each 45 degrees.
4. Therefore, all four angles in Rhombus 2 measure 45 degrees.
Rhombus 3:
1. Following the same steps as for Rhombus 1, we can determine that angles 10 and 12 are equal, and angles 11 and 13 are equal.
2. Angles 10 and 11 are complementary, so angles 10 and 12 are each 45 degrees (half of 90 degrees).
3. Angles 11 and 13 are also each 45 degrees.
4. Therefore, all four angles in Rhombus 3 measure 45 degrees.
Rhombus 4:
1. Following the same steps as for Rhombus 1, we can determine that angles 14 and 17 are equal, and angles 15 and 16 are equal.
2. Angles 14 and 15 are complementary, so angles 14 and 17 are each 45 degrees (half of 90 degrees).
3. Angles 15 and 16 are also each 45 degrees.
4. Therefore, all four angles in Rhombus 4 measure 45 degrees.
Conclusion:
All four angles in each of the four rhombuses measure 45 degrees.