Question

which choice below shows all the lines of symmetry for the figure? images of hexagons if the figure has rotational symmetry, tell the angle of rotation. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the angle of rotation is \boxed{}° (type an integer or a decimal) b. the figure does not have rotational symmetry. d. the figure has no lines of symmetry.

Explanation:

Part 1: Lines of Symmetry for a Regular Hexagon

A regular hexagon has 6 lines of symmetry. Let's analyze the options:

• Option A: Likely shows fewer than 6 lines (maybe 3 or 6 but misdrawn? No, the correct one should have 6 lines of symmetry, with 3 through opposite vertices and 3 through midpoints of opposite sides. Wait, looking at the figures, the correct figure (let's assume the middle one, B) has 6 lines of symmetry (since a regular hexagon has 6). So the correct choice for "Which choice below shows all the lines of symmetry for the figure?" is the one with 6 lines (probably option B, as a regular hexagon has 6 lines of symmetry: 3 through vertices and 3 through mid - sides).

Part 2: Rotational Symmetry of a Regular Hexagon

Step 1: Recall the formula for rotational symmetry angle

The formula for the angle of rotational symmetry of a regular polygon with \(n\) sides is \(\theta=\frac{360^{\circ}}{n}\).
For a hexagon, \(n = 6\).

Step 2: Calculate the angle

Substitute \(n = 6\) into the formula: \(\theta=\frac{360^{\circ}}{6}=60^{\circ}\). Also, the hexagon has rotational symmetry, so we choose option A and fill in the angle.

A regular hexagon has rotational symmetry. The angle of rotation is calculated by dividing \(360^{\circ}\) by the number of sides (\(n = 6\)).

Step 1: Use the rotational symmetry formula

The formula for the angle of rotational symmetry of a regular \(n\) - sided polygon is \(\theta=\frac{360^{\circ}}{n}\). For a hexagon, \(n = 6\).

Step 2: Compute the angle

\(\theta=\frac{360^{\circ}}{6}=60^{\circ}\)

Answer:

(for lines of symmetry): The correct option for lines of symmetry is the one with 6 lines (e.g., if B is the one with 6 lines, then B. [Description of B's figure, e.g., the figure with 6 lines of symmetry passing through vertices and mid - sides]).