If all the angles of a quadrilateral are less than 180°, then the quadrilateral is a:

Question

Accepted Answer

In the context of the given question, we are tasked with identifying the type of quadrilateral where all angles are less than 180°. The correct answer is Option 1: Convex quadrilateral. Let's explore why this is the correct choice and why the other options are not applicable.

1. **Convex Quadrilateral (Option 1):**
   - A convex quadrilateral is defined as a quadrilateral where all interior angles are less than 180°. This means that no angle in the quadrilateral points inward, and the shape does not "cave in" at any point. The sum of the interior angles of any quadrilateral is always 360°, and in a convex quadrilateral, each angle contributes to this sum without exceeding 180°. Therefore, if all angles are less than 180°, the quadrilateral is indeed convex, making Option 1 the correct answer.

2. **Concave Quadrilateral (Option 2):**
   - A concave quadrilateral has at least one interior angle greater than 180°. This causes the shape to have a "caved-in" appearance, where one of the vertices points inward. Since the question specifies that all angles are less than 180°, a concave quadrilateral cannot be the correct answer.

3. **Parallelogram (Option 3):**
   - A parallelogram is a specific type of quadrilateral where opposite sides are parallel. While it is true that the angles in a parallelogram can be less than 180°, the definition of a parallelogram does not inherently require all angles to be less than 180°. Therefore, while a parallelogram can be convex, the term "parallelogram" does not specifically address the condition of all angles being less than 180°, making it an incorrect choice in this context.

4. **Trapezium (Option 4):**
   - A trapezium (or trapezoid in some regions) is a quadrilateral with at least one pair of parallel sides. Similar to a parallelogram, a trapezium can have angles less than 180°, but the definition does not specifically ensure that all angles are less than 180°. Thus, it does not directly satisfy the condition given in the question, making it an incorrect option.

In conclusion, the only option that directly aligns with the condition that all angles of the quadrilateral are less than 180° is a convex quadrilateral. Therefore, Option 1 is the correct answer.