To solve for the value of $X$ in this diagram, let's analyze the given information.

Step 1: Understanding the Diagram

• The diagram appears to depict a quadrilateral with some angles labeled:
  • One angle is labeled $95^\circ$.
  • Another angle is labeled $X^\circ$.
  • The quadrilateral has an additional angle that is $90^\circ$ (indicated by the square marking).

Step 2: Applying the Sum of Interior Angles in a Quadrilateral

• The sum of the interior angles of any quadrilateral is always $360^\circ$.

Step 3: Setting Up the Equation

• Denote the four angles of the quadrilateral as:

  1. $X^\circ$ (the angle we need to find)
  2. $95^\circ$ (given)
  3. $90^\circ$ (given)
  4. The fourth angle, let's call it $\theta$, which is also marked on the diagram.

• The equation for the sum of the angles is: $X + 95^\circ + 90^\circ + \theta = 360^\circ$

Step 4: Solving for $X$

• The fourth angle $\theta$ is given as $105^\circ$ (based on what seems to be visible from the diagram).

• Substitute the known angles into the equation: $X + 95^\circ + 90^\circ + 105^\circ = 360^\circ$

• Combine the known angles: $X + 290^\circ = 360^\circ$

• Subtract $290^\circ$ from both sides: $X = 70^\circ$

Final Answer

• The value of $X$ is $70^\circ$.

Would you like further explanation or have any additional questions? Here are some related questions to consider:

1. What are the steps to find an unknown angle in any polygon?
2. How does the sum of interior angles vary with different polygons?
3. What is the relationship between supplementary angles and quadrilaterals?
4. How does the right angle (90°) influence the calculation in this problem?
5. Can this method be applied to irregular quadrilaterals, and how?

Tip: When solving problems involving polygons, remember that the sum of the interior angles depends on the number of sides, and this can often simplify calculations!