Quiz Topic:Understanding Quadrilateral.....By Neelam Mam

A nonagon is a polygon with nine sides and nine angles. The term comes from the Latin word "nonus," meaning ninth, and "gon," meaning angle. In geometry, polygons are named based on the number of sides they have, and a nonagon is specifically defined as a nine-sided figure. This makes it a relatively simple yet distinct shape in the study of polygons, following the naming conventions for geometric shapes.

A quadrilateral whose all sides, diagonals, and angles are equal is a square. A square is a special type of quadrilateral where all four sides are equal in length, all four angles are right angles (90 degrees), and the diagonals are also equal in length and bisect each other at right angles. This unique combination of equal sides, equal angles, and equal diagonals distinguishes a square from other quadrilaterals such as trapeziums, rectangles, and rhombuses.

A five-sided polygon is known as a pentagon.

A triangle is a polygon with three sides and three angles. The sum of the measures of the three angles in a triangle is always 180 degrees. Therefore, the given statement is correct.

The diagonals of a parallelogram bisect each other. This means that the diagonals divide each other into two equal parts.

The sum of all exterior angles of a triangle is always equal to 360 degrees. This is a well-known property of triangles, where each exterior angle is equal to the sum of the two opposite interior angles. Therefore, the correct answer is 3600.

In a parallelogram, adjacent angles are supplementary, meaning their measures add up to 180 degrees. This property arises because opposite sides of a parallelogram are parallel, making consecutive angles on a straight line equal to 180 degrees. For instance, if one angle is 70 degrees, the adjacent angle must be 110 degrees to total 180 degrees, ensuring the supplementary nature of adjacent angles in any parallelogram.

A quadrilateral is a polygon with four sides. An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. In a quadrilateral, there are four angles. To maximize the number of obtuse angles, we need to minimize the number of acute angles (angles less than 90 degrees). Since there must be at least one acute angle in a quadrilateral, we can have a maximum of three obtuse angles. Therefore, the correct answer is 3.

A hexagon is a polygon with six sides. To find the number of diagonals, we need to consider that each vertex can be connected to every other vertex except the adjacent ones. In a hexagon, there are six vertices, so each vertex can be connected to four other vertices. However, we need to divide this number by 2 because each diagonal is counted twice (from both ends). Therefore, the total number of diagonals in a hexagon is (6 * 4) / 2 = 12 / 2 = 6.