In a quadrilateral, three interior angles measure 60°, 90°, and 100°. What is the measure of the fourth interior angle of the quadrilateral in degrees?

Introduction / Context:
This problem checks understanding of the sum of interior angles in a quadrilateral. Such questions are standard in school level geometry and aptitude tests and help reinforce basic polygon angle sum formulas, which are very useful in more advanced geometry problems as well.

Given Data / Assumptions:
- The figure is a quadrilateral, so it has four interior angles.
- Three interior angles are given as 60°, 90°, and 100°.
- We need to find the measure of the fourth interior angle in degrees.

Concept / Approach:
For any polygon with n sides, the sum of interior angles is (n − 2) * 180 degrees. For a quadrilateral, n = 4, so the sum of interior angles is:
Sum = (4 − 2) * 180 = 2 * 180 = 360 degrees.
Once we know this total, we subtract the sum of the three known angles from 360 degrees in order to obtain the missing fourth angle.

Step-by-Step Solution:
Step 1: Write the general formula for a quadrilateral: sum of interior angles = 360°. Step 2: Add the three given angles: 60° + 90° + 100°. Step 3: Compute this sum: 60° + 90° = 150°, and 150° + 100° = 250°. Step 4: Subtract this from the total: 360° − 250° = 110°. Step 5: Therefore, the fourth interior angle of the quadrilateral is 110°.

Verification / Alternative Check:
We can verify by adding all four angles including the found value. So, 60° + 90° + 100° + 110° = 360°. This matches the known interior angle sum of a quadrilateral, confirming that 110° is correct. No other angle in the options will satisfy this basic angle sum requirement.

Why Other Options Are Wrong:
Option a, 95°, would give total 60° + 90° + 100° + 95° = 345°, which is less than 360°, so it cannot be correct.
Option b, 100°, would give 60° + 90° + 100° + 100° = 350°, still not 360°.
Option d, 115°, would give 60° + 90° + 100° + 115° = 365°, which is greater than 360°, so it also fails.

Common Pitfalls:
Learners sometimes confuse the formula for the sum of angles in a quadrilateral with that of a triangle. Another common error is arithmetic, such as adding the three known angles incorrectly or subtracting from 180° instead of 360°. Carefully remembering that a quadrilateral can be split into two triangles helps, because 2 * 180° clearly shows that the total must be 360°.

Final Answer:
The fourth interior angle of the quadrilateral is 110°.