No because , The sum of the four interior angles of a quadrilateral must be equal to 360 degree. So, a quadrilateral cannot be formed.

Understanding Quadrilaterals
In geometry, a quadrilateral is a four-sided polygon. The sum of the interior angles of any quadrilateral is always 360 degrees. To determine if a quadrilateral can have angles measuring 105 degrees each, let’s break down the situation.
Sum of Angles in a Quadrilateral
- The total measure of angles in a quadrilateral = 360 degrees.
Angles of 105 Degrees
- If we consider a quadrilateral with four angles measuring 105 degrees:
- Angle 1 = 105 degrees
- Angle 2 = 105 degrees
- Angle 3 = 105 degrees
- Angle 4 = 105 degrees
Calculating the Total Measure
- Total angle measure = 105 + 105 + 105 + 105 = 420 degrees.
Conclusion
- Since 420 degrees exceeds the required 360 degrees, it is impossible to have a quadrilateral with all angles measuring 105 degrees.
Possible Angles for a Quadrilateral
- Instead, the angles must be varied to ensure their sum equals 360 degrees. For example:
- Angle 1 = 90 degrees
- Angle 2 = 90 degrees
- Angle 3 = 90 degrees
- Angle 4 = 90 degrees
- Total = 360 degrees.
Final Thoughts
- Quadrilaterals can have various combinations of angles, but they must always satisfy the rule that their sum is 360 degrees. Thus, a quadrilateral cannot consist solely of angles measuring 105 degrees.
This understanding is crucial for solving problems related to quadrilaterals in geometry.