Give reasons
1) Every parallelogram is not a rectangle.
2) Every rhombus is not square.
3)It is possible to have exterior angle of a regular polygon as 40 degree.
4) It is not possible to have interior angle of regular polygon as 145 degree.
1) The angles of a parallelogram do not have to be right angles.
2) The angles of a rhombus do not have to be right angles.
3) For a regular polygon, the exterior angle must be evenly divisible into 360. In this case it is, and you have a nine-sided figure.
4) The supplement of 145 is 35 degrees. That would have to the the exterior angle. It is not evenly divisible into 360 degrees, and so 145 cannot be the interior angle of a regular polygon.
1) To determine whether every parallelogram is not a rectangle, you need to understand the properties of parallelograms and rectangles.
A parallelogram is a quadrilateral with opposite sides that are parallel. It has two pairs of equal and parallel sides but its angles can vary.
On the other hand, a rectangle is a parallelogram with four right angles (90 degrees each). This means that all rectangles are parallelograms, but not all parallelograms are rectangles.
To demonstrate this, you can draw different parallelograms with equal and parallel sides, but with angles that are different from 90 degrees. This would prove that not every parallelogram is a rectangle.
2) To determine whether every rhombus is not a square, you need to understand the properties of rhombuses and squares.
A rhombus is a quadrilateral with all sides of equal length. It has opposite sides that are parallel but its angles can vary.
A square, on the other hand, is a special case of a rhombus where all angles are right angles (90 degrees) and all sides are equal in length.
Thus, while all squares are rhombuses, not all rhombuses are squares. You can visualize this by drawing a rhombus with equal sides but angles that are not 90 degrees.
3) To determine whether it is possible to have an exterior angle of a regular polygon as 40 degrees, you can use the formula for the exterior angle of a regular polygon: 360 degrees divided by the number of sides.
For example, if we have a regular polygon with 8 sides (an octagon), each exterior angle would be 360 degrees divided by 8, which equals 45 degrees.
Since 40 degrees is smaller than 45 degrees, it is indeed possible to have an exterior angle of a regular polygon as 40 degrees. You can verify this by drawing an 8-sided polygon and measuring one of its exterior angles with a protractor.
4) To determine whether it is possible to have an interior angle of a regular polygon as 145 degrees, you can use the formula for the interior angle of a regular polygon: 180 degrees times (n-2), where n is the number of sides.
For example, if we have a regular polygon with 7 sides (a heptagon), each interior angle would be 180 degrees times (7-2), which equals 900 divided by 7, resulting in approximately 128.57 degrees.
Since 145 degrees is larger than 128.57 degrees, it is possible to have an interior angle of a regular polygon as 145 degrees. You can verify this by drawing a 7-sided polygon and measuring one of its interior angles with a protractor.