The short diagonal is the line between two vertices, which have a third vertex between them. Its length equals that of the height. The long diagonal is the line between two opposite vertices.

No, as a general rule the diagonals of a parallelogram do not bisect each other at right angles. The definition of a parallelogram is a four-sided polygon with opposite sides parallel and equal in length. For all parallelograms that are not squares, the diagonals do not intersect at right angles.

It turns out that a parallelogram has its diagonals meeting at right angles if and only if the parallelogram is a rhombus (all sides equal). Note that a square is a special case of a rhombus. If the angle at which they meet is 90∘, then by the Pythagorean Theorem each side of the rectangle has length √p2+q2.

Rhombus

• A rhombus has four sides of equal lengths.
• It has two pairs of equal angles.
• The opposite sides are parallel.
• The diagonals bisect each other at right angles.

Explanation: Regular hexagons are comprised of six equilateral triangles; in our question, these triangles each have side length 4 (see diagram). The length of a diagonal is equal to two times the length of the side. In this instance, the answer is 8.

Since, an obtuse angle is greater than 900 but smaller than 1800 . So, this means that 1080 must be an obtuse angle. Since, here there are a total five 1080 angles in the pentagon, so we can say that there are five obtuse angles in a regular pentagon. Hence, there are total 5 obtuse angles in a regular pentagon.

Since it’s a regular hexagon (six-sided polygon), we know it’s made up of sets of parallel lines. The interior angle of the hexagon is supplementary to ∠1 because they form a linear pair, so the measure of one interior angle of the hexagon is 180 – m∠1, or 120°.