To solve the problem in the image, we need to determine the missing angle $X$ in the given quadrilateral. Here's the detailed process:

Step 1: Understand the properties of the quadrilateral

In a quadrilateral, the sum of all interior angles is always $360^\circ$. This rule applies regardless of the type of quadrilateral.

Step 2: Identify known angles

The given angles in the quadrilateral are:

• $\angle A = 85^\circ$,
• $\angle B = 80^\circ$,
• $\angle C = 75^\circ$,
• $\angle D = X$ (unknown).

Step 3: Apply the angle sum property

Using the property: $\angle A + \angle B + \angle C + \angle D = 360^\circ$ Substitute the known values: $85^\circ + 80^\circ + 75^\circ + X = 360^\circ$

Step 4: Solve for $X$

Simplify: $240^\circ + X = 360^\circ$ $X = 360^\circ - 240^\circ$ $X = 120^\circ$

Final Answer

The missing angle $X$ is: $\boxed{120^\circ}$

Would you like further clarification or an alternative explanation?

Related Questions

1. What is the formula for the sum of angles in any polygon?
2. How would the solution change if one angle was instead labeled as $2X$?
3. Why is the sum of the interior angles of a quadrilateral always $360^\circ$?
4. Can this method be applied to irregular quadrilaterals?
5. What is the difference in angle calculation for quadrilaterals and triangles?

Tip: Always double-check that all angles are accounted for and sum correctly when solving for missing angles in polygons!