What is the maximum number of obtuse angles that a quadrilateral has?

• A. 1
• B. 2
• C. 3
• D. 4

The maximum number of obtuse angles in a quadrilateral is limited by the properties of angles in a polygon. A quadrilateral has four angles, and the sum of these angles is always 360 degrees.

Understanding Obtuse Angles

An obtuse angle is one that measures more than 90 degrees but less than 180 degrees. If a quadrilateral were to have more than two obtuse angles, the total angle measure would exceed 360 degrees, which is not possible.

Analyzing the Options

• 1 obtuse angle: Possible, as the other three angles can be acute.
• 2 obtuse angles: Also possible, with the remaining two angles being acute.
• 3 obtuse angles: This configuration would lead to a total angle sum greater than 360 degrees, which is not feasible.
• 4 obtuse angles: This is impossible, as it would require a total angle sum of at least 360 degrees.

Final Answer

Therefore, the maximum number of obtuse angles that a quadrilateral can have is 2.