Question

what is the minimum angle of rotation for which a regular pentagon exhibits rotational symmetry?
a. 180 degrees
b. 360 degrees
c. 72 degrees
d. 90 degrees
how many lines of symmetry does an equilateral triangle have?
a. 5
b. 1
c. 3
d. 0
how many lines of symmetry does a regular hexagon have?
a. 2
b. 4
c. 6
d. 3
which shape does not typically display reflective symmetry?
a. equilateral triangle
b. square
c. circle
d. scalene triangle

Explanation:

Step1: Recall rotation - symmetry formula

For a regular polygon with \(n\) sides, the minimum rotation - angle \(\theta=\frac{360^{\circ}}{n}\). For a pentagon, \(n = 5\), so \(\theta=\frac{360^{\circ}}{5}=72^{\circ}\).

Step2: Recall lines - of - symmetry of equilateral triangle

An equilateral triangle has 3 lines of symmetry (bisecting each vertex to the mid - point of the opposite side).

Step3: Recall lines - of - symmetry of regular hexagon

A regular hexagon has 6 lines of symmetry (3 through opposite vertices and 3 through mid - points of opposite sides).

Step4: Recall reflective symmetry

A scalene triangle has no equal sides or angles, so it has no lines of reflective symmetry.

Answer:

1. C. 72 degrees
2. C. 3
3. C. 6
4. D. Scalene triangle