All questions of Understanding Quadrilaterals for Class 8 Exam

Each polygon have 360• as it's exterior angel but it's Interior angle is depend on it's sides, so the answer is D

D)

Explanation:
A rhombus is a quadrilateral with all sides equal in length. It is also known as a diamond shape. The diagonals of a rhombus are the line segments that connect opposite vertices of the rhombus.

The diagonals of a rhombus have some important properties:

1. The diagonals of a rhombus bisect each other at right angles. This means that the point where the diagonals intersect is the midpoint of each diagonal, and the diagonals form four right angles.

2. The diagonals of a rhombus are equal in length. This is because a rhombus has four sides of equal length, and the diagonals connect opposite vertices, which are also equidistant from the center of the rhombus.

3. The diagonals of a rhombus are perpendicular bisectors of each other. This means that each diagonal divides the other diagonal into two equal parts, and each diagonal is perpendicular to the other diagonal.

Therefore, we can conclude that the correct answer is option C, which states that the diagonals of a rhombus are perpendicular bisectors of each other.

• Polygon: A polygon is a closed figure made up of line segments. It can have any number of sides, including triangles, quadrilaterals, pentagons, and so on.


• Quadrilateral: A quadrilateral is a polygon with four sides and four angles. It is a specific type of polygon, not a general closed curve made up of line segments.


• Hexagon: A hexagon is a polygon with six sides and six angles. Like the quadrilateral, it is a specific type of polygon and not a general closed curve made up of line segments.


• None of these: This option does not apply as the correct answer is A - polygon.

Therefore, the correct answer is A: polygon. A simple closed curve made up of only line segments is called a polygon.

A noun and a verb.

Sum of all angles of a quadrilateral is 360 degree . so we will add all the angles of quadrilateral and subtract it from 360 to get x. there is a linear pair on left side and exterior angle is 90 hence the other angle will be 90 by linear pair property. hence 70+60+90+x=360 220+x=360 x=360-220 x=140 hence C is the right answer.

Understanding Exterior Angles of a Polygon
To find the measure of each exterior angle of a regular polygon, we can use a simple formula. An exterior angle is formed by one side of the polygon and the extension of an adjacent side.
Formula for Exterior Angles
The formula to calculate the measure of each exterior angle of a regular polygon is:
- Each exterior angle = 360° / Number of sides
In this case, we have a regular polygon with 9 sides.
Calculation Steps
1. Identify the number of sides:
- This polygon has 9 sides.
2. Apply the formula:
- Each exterior angle = 360° / 9
3. Perform the calculation:
- 360° ÷ 9 = 40°
Conclusion
Therefore, the measure of each exterior angle of a regular polygon with 9 sides is 40°.
This means the correct answer is option 'C', which is 40°.
Understanding this concept helps in various applications, including geometry and real-world situations where shapes are involved.

A rhombus has all the properties of a parallelogram and also that of a kite. Let's break down the properties of each shape to understand why a rhombus fits the description.

**Properties of a Parallelogram:**
1. Opposite sides are parallel: In a parallelogram, opposite sides are always parallel. This means that if you extend the sides of a parallelogram, they will never intersect.

2. Opposite sides are congruent: The lengths of opposite sides in a parallelogram are equal. This implies that if you measure the length of one side and compare it to the length of the opposite side, they will be the same.

3. Opposite angles are congruent: The angles formed by the intersection of the sides in a parallelogram are equal. If you measure one angle and compare it to the angle opposite it, they will have the same measure.

4. Consecutive angles are supplementary: The sum of two consecutive angles in a parallelogram is always 180 degrees. For example, if angle A and angle B are consecutive angles in a parallelogram, then angle A + angle B = 180 degrees.

**Properties of a Kite:**
1. Two pairs of adjacent sides are congruent: In a kite, two consecutive sides are equal in length. This means that if you measure the length of one side and compare it to the length of the side next to it, they will be the same.

2. One pair of opposite angles is congruent: The angles formed by the intersection of the sides in a kite are equal. If you measure one angle and compare it to the angle opposite it, they will have the same measure.

3. Diagonals are perpendicular: The diagonals of a kite are perpendicular to each other. This means that if you draw the diagonals of a kite, they will intersect at a right angle.

Based on these properties, a rhombus fits the description of having all the properties of a parallelogram and also that of a kite.

In a rhombus:
- Opposite sides are parallel (parallelogram property).
- Opposite sides are congruent (parallelogram property).
- Opposite angles are congruent (parallelogram property).
- Consecutive angles are supplementary (parallelogram property).
- Two pairs of adjacent sides are congruent (kite property).
- One pair of opposite angles is congruent (kite property).
- Diagonals are perpendicular (kite property).

Therefore, a rhombus is the correct answer as it encompasses all the properties of both a parallelogram and a kite.

Explanation:

A diagonal is a line segment that connects two nonadjacent vertices of a polygon. In the case of a triangle, a diagonal would connect two vertices that are not adjacent to each other.

A triangle has three sides and three vertices. Let's label the vertices as A, B, and C.

To count the number of diagonals, we need to connect each vertex to every other vertex that is not adjacent to it.

Connecting vertex A:
- A cannot be connected to itself, so we eliminate one possibility.
- A can be connected to B, which forms one diagonal.
- A can be connected to C, which forms another diagonal.

Connecting vertex B:
- B cannot be connected to itself, so we eliminate one possibility.
- B can be connected to A, which forms one diagonal.
- B can be connected to C, which forms another diagonal.

Connecting vertex C:
- C cannot be connected to itself, so we eliminate one possibility.
- C can be connected to A, which forms one diagonal.
- C can be connected to B, which forms another diagonal.

Total number of diagonals:
Adding up all the possibilities, we have a total of 2 + 2 + 2 = 6 diagonals.

However, we need to remember that a diagonal must connect two nonadjacent vertices. In a triangle, all the vertices are adjacent to each other. Therefore, no diagonals can be formed within a triangle.

Hence, the correct answer is option C: 0 diagonals.

How it is supplementary angle 

In a parallelogram, opposite sides are equal in length.

Therefore, AB = CD and AD = BC.

Given that AB = 2x + 5, CD = y + 1, AD = y + 5, and BC = 3x, we can set up two equations:

2x + 5 = y + 1 (equation 1)
y + 5 = 3x (equation 2)

From equation 1, we can isolate y:

y = 2x + 4

Substituting this value of y into equation 2, we get:

2x + 4 + 5 = 3x

Simplifying, we have:

9 = x

Now we can substitute this value of x back into the equations to find the lengths of the sides:

AB = 2(9) + 5 = 23
CD = y + 1 = (2(9) + 4) + 1 = 23
AD = y + 5 = (2(9) + 4) + 5 = 27
BC = 3(9) = 27

So, the lengths of the sides are AB = 23, CD = 23, AD = 27, and BC = 27.

A) Pentagon have 5 sides B) Hexagon have 6 sides C) Heptagon have 7 sides So the correct answer is B.