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14 10. (i)

A B C D E F

is a regular hexagon. a) Find the value of an exteri...

Mar 15, 2024

14 10. (i)

A B C D E F

is a regular hexagon. a) Find the value of an exterior angle Answer (2) b) Find the value of an interior angle Answer (2) c) Find the number of lines of symmetry Answer [1] d) Find the order of rotational symmetry Answer [1] Boyal Institute International School

Solution by Steps

step 1

To find the value of an exterior angle of a regular hexagon, we use the fact that the sum of exterior angles of any polygon is 360°. Since a hexagon has 6 sides, each exterior angle is equal to 360° divided by 6

step 2

Calculating the value of one exterior angle:

\frac{360°}{6} = 60°

Answer

60°

Key Concept

Exterior Angle of a Regular Polygon

Explanation

The exterior angles of any regular polygon sum up to 360°, and since a hexagon has 6 sides, each exterior angle is 360°/6.

Solution by Steps

step 1

To find the value of an interior angle of a regular hexagon, we use the fact that the sum of interior angles of a polygon with n sides is given by (n-2) × 180°. For a hexagon, n = 6

step 2

Calculating the sum of interior angles:

(6-2) \times 180° = 4 \times 180° = 720°

step 3

Since all interior angles in a regular hexagon are equal, each interior angle is the total sum divided by 6:

\frac{720°}{6} = 120°

Answer

120°

Key Concept

Interior Angle of a Regular Polygon

Explanation

The sum of interior angles of a polygon is (n-2) × 180°, and for a regular hexagon, each interior angle is one-sixth of this sum.

Solution by Steps

step 1

To find the number of lines of symmetry of a regular hexagon, we observe that a regular hexagon has a line of symmetry through each vertex and the opposite side

step 2

Counting the lines of symmetry: A regular hexagon has 6 vertices, so it has 6 lines of symmetry

Answer

Key Concept

Lines of Symmetry in Regular Polygons

Explanation

A regular hexagon has 6 lines of symmetry, one for each vertex and its opposite side.

Solution by Steps

step 1

To find the order of rotational symmetry of a regular hexagon, we determine how many times the hexagon maps onto itself during a full 360° rotation

step 2

Calculating the order of rotational symmetry: A regular hexagon maps onto itself every 60° (360°/6), so it has an order of rotational symmetry of 6

Answer

Key Concept

Rotational Symmetry of Regular Polygons

Explanation

The order of rotational symmetry of a regular polygon is equal to the number of sides the polygon has. For a hexagon, this is 6.