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The problem in the image asks to determine the unknown angle of a quadrilateral, where three angles are given: 80°, 75°, and 105°.

To solve this:

1. The sum of the interior angles of any quadrilateral is always **360°**.
   
2. The three given angles are: 
   - 80°
   - 75°
   - 105°

3. To find the unknown angle \( x \), we subtract the sum of the known angles from 360°:
   \[
   x = 360° - (80° + 75° + 105°)
   \]
   \[
   x = 360° - 260° = 100°
   \]

So, the unknown angle is **100°**, which means the selected answer of 90° is incorrect. The correct answer should be **100°**.

Would you like further details on this? Here are some additional related questions:

1. What is the sum of the interior angles of a pentagon?
2. How do you find the sum of the angles in a polygon?
3. Can a quadrilateral have two angles larger than 180°?
4. What properties do trapezoids have in terms of angles?
5. How can we verify if a quadrilateral is cyclic based on its angles?

**Tip:** Always double-check the sum of the given angles to ensure you haven't made calculation errors when determining the unknown angle.

Determine the unknown angle measurement of the quadrilateral below.

Solve the problem to find the unknown angle in a quadrilateral where three angles are given: 80°, 75°, and 105°. Understand the angle sum property and use it to determine the correct answer. Suitable for Grade 7 students.

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