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All questions of Understanding Shapes for Class 8 Exam

What is the primary characteristic of a simple closed curve?
  • a)
    It must be a polygon.
  • b)
    It encloses two separate areas.
  • c)
    It can have overlapping lines.
  • d)
    It does not cross itself.
Correct answer is option 'D'. Can you explain this answer?

Trisha Vashisht answered
A simple closed curve is defined by the fact that it does not cross itself at any point, thereby enclosing a single area without overlapping lines. This property distinguishes simple closed curves from other types of curves and is critical in various geometric analyses. Examples include circles and simple polygons.
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In a regular hexagon, what is the measure of each interior angle?
  • a)
    180°
  • b)
    120°
  • c)
    150°
  • d)
    90°
Correct answer is option 'B'. Can you explain this answer?

Trisha Vashisht answered
In a regular hexagon, each interior angle can be calculated using the formula for the sum of interior angles, which is (n - 2) × 180°. For a hexagon (6 sides), the total is (6 - 2) × 180° = 720°. Since all angles are equal in a regular hexagon, each interior angle measures 720° / 6 = 120°. This uniformity contributes to the hexagon's symmetry and appeal in both mathematics and design.

What is the primary difference between a convex polygon and a regular polygon?
  • a)
    Convex polygons must have at least one angle greater than 180°.
  • b)
    Regular polygons can only have four sides, while convex can have any number.
  • c)
    Convex polygons have equal sides, and regular polygons do not.
  • d)
    Convex polygons have all angles less than 180°, while regular polygons also have equal sides and angles.
Correct answer is option 'D'. Can you explain this answer?

Trisha Vashisht answered
The primary difference is that while convex polygons have all interior angles less than 180°, regular polygons not only have this property but also possess equal side lengths and equal angles. This distinction is crucial for classifying polygons in geometry and understanding their properties. Regular polygons exhibit a high degree of symmetry, which makes them a fascinating subject of study.

What is a defining characteristic of a polygon?
  • a)
    It is a closed figure made of straight line segments.
  • b)
    It can be formed by curved lines.
  • c)
    It must have only three sides.
  • d)
    It has at least one angle greater than 180°.
Correct answer is option 'A'. Can you explain this answer?

EduRev Class 8 answered
A polygon is defined as a closed shape formed by straight line segments, which meet only at their endpoints called vertices. This characteristic distinguishes polygons from other shapes that may include curves or open lines. An interesting fact about polygons is that they can be classified based on the number of sides they have, such as triangles (3 sides) and quadrilaterals (4 sides).

What is the sum of the interior angles of a quadrilateral?
  • a)
    180°
  • b)
    720°
  • c)
    360°
  • d)
    540°
Correct answer is option 'C'. Can you explain this answer?

EduRev Class 8 answered
The sum of the interior angles of a quadrilateral is always 360°. This can be proven by dividing the quadrilateral into two triangles, each contributing 180°, resulting in a total of 360°. This property is fundamental in geometry and is frequently used in various applications involving four-sided figures.

Which of the following best describes a closed curve?
  • a)
    It encloses an area.
  • b)
    It cannot be formed by line segments.
  • c)
    It has endpoints.
  • d)
    It is always straight.
Correct answer is option 'A'. Can you explain this answer?

EduRev Class 8 answered
A closed curve is defined as a curve that connects back to itself, thereby enclosing an area. This characteristic means that closed curves do not have endpoints, as they form a complete boundary around a region. Examples of closed curves include circles and polygons. Understanding closed curves is essential in geometry, particularly in calculating areas.

What is the relationship between the number of sides of a regular polygon and its exterior angles?
  • a)
    Each exterior angle is equal to 180° divided by the number of sides.
  • b)
    Each exterior angle is equal to 360° divided by the number of sides.
  • c)
    There is no relationship.
  • d)
    The number of sides is equal to the measure of each exterior angle.
Correct answer is option 'B'. Can you explain this answer?

Trisha Vashisht answered
The measure of each exterior angle of a regular polygon is equal to 360° divided by the number of sides. This relationship allows you to easily determine the size of each exterior angle based on how many sides the polygon has. This property is useful for understanding the overall shape and symmetry of regular polygons.

What is an example of an open curve?
  • a)
    Triangle
  • b)
    Rectangle
  • c)
    Straight line segment
  • d)
    Circle
Correct answer is option 'C'. Can you explain this answer?

Trisha Vashisht answered
An open curve is a line that does not connect back to itself, meaning it has two distinct endpoints and does not enclose any area. A straight line segment is a clear example of an open curve. In contrast, closed curves like circles or triangles enclose a space. It's fascinating how open curves can be easily extended indefinitely without forming a closed shape.

Which type of polygon has all its interior angles less than 180°?
  • a)
    Regular Polygon
  • b)
    Convex Polygon
  • c)
    Irregular Polygon
  • d)
    Concave Polygon
Correct answer is option 'B'. Can you explain this answer?

EduRev Class 8 answered
A convex polygon is defined by the property that all its interior angles are less than 180°. This means that all vertices point outward, and no part of the shape bends inward. An interesting aspect of convex polygons is that they can be divided into triangles without leaving any parts outside the polygon.

Which of the following is true about a regular polygon?
  • a)
    All sides and angles are equal.
  • b)
    All interior angles are unequal.
  • c)
    All sides are of different lengths.
  • d)
    It must have at least six sides.
Correct answer is option 'A'. Can you explain this answer?

EduRev Class 8 answered
A regular polygon is defined by having all sides equal in length and all interior angles equal as well. This uniformity makes regular polygons particularly interesting in geometry, as they exhibit symmetry and can often be inscribed in circles. An example of a regular polygon is a square, which has four equal sides and four right angles.

If a polygon has 6 sides, what is the sum of its interior angles?
  • a)
    540°
  • b)
    720°
  • c)
    180°
  • d)
    360°
Correct answer is option 'B'. Can you explain this answer?

Trisha Vashisht answered
The sum of the interior angles of a polygon with 'n' sides is calculated using the formula (n - 2) × 180°. For a hexagon (6 sides), the calculation is (6 - 2) × 180° = 4 × 180° = 720°. Understanding this helps in solving various geometry problems related to polygons.

Which polygon is characterized by having at least one interior angle greater than 180°?
  • a)
    Simple Polygon
  • b)
    Regular Polygon
  • c)
    Concave Polygon
  • d)
    Convex Polygon
Correct answer is option 'C'. Can you explain this answer?

EduRev Class 8 answered
A concave polygon is defined by having at least one interior angle greater than 180°, meaning that at least one vertex points inward, creating a "dent" in the shape. This property contrasts with convex polygons, where all angles are less than 180°. Concave polygons can create interesting geometric designs due to their inward angles.

How many sides does a pentagon have?
  • a)
    3
  • b)
    5
  • c)
    6
  • d)
    4
Correct answer is option 'B'. Can you explain this answer?

EduRev Class 8 answered
A pentagon is a polygon that has exactly five sides and five vertices. This classification is part of the larger family of polygons, and knowing the number of sides helps in identifying the specific type of polygon. Interestingly, regular pentagons have equal sides and angles, which contribute to their aesthetic appeal in design and architecture.

What distinguishes a convex polygon from a concave polygon?
  • a)
    Concave polygons have all angles equal.
  • b)
    Convex polygons have more than 6 sides.
  • c)
    All angles in a convex polygon are less than 180°.
  • d)
    Convex polygons can have indentations.
Correct answer is option 'C'. Can you explain this answer?

EduRev Class 8 answered
The distinguishing feature of a convex polygon is that all its interior angles are less than 180°, meaning that all vertices point outward. In contrast, concave polygons have at least one interior angle greater than 180°, leading to an inward-pointing vertex. This distinction is fundamental in classifying polygons in geometry.

What is the sum of the exterior angles of any polygon?
  • a)
    180°
  • b)
    n × 180°
  • c)
    (n - 2) × 180°
  • d)
    360°
Correct answer is option 'D'. Can you explain this answer?

Trisha Vashisht answered
The sum of the exterior angles of any polygon, regardless of the number of sides, is always 360°. This property holds true due to the way exterior angles are formed by extending the sides of the polygon. This consistent characteristic of polygons is a key concept in geometry and helps in various calculations involving shapes.

Chapter doubts & questions for Understanding Shapes - Mathematics Class 8 ICSE 2025 is part of Class 8 exam preparation. The chapters have been prepared according to the Class 8 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 8 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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