Abcdefgh is a regular octagon. the minimum degree of rotation by which this octagon can map onto itself is (30 ; 45 ; 90 ; 120 °). it will take ( 2 ; 4 ; 6 ; 8 ) increments of that degree of clockwise rotation for a′ (the image of a) to coincide with c.

45°

2 - Clockwise

Step-by-step explanation:

ABCDEFGH is a regular octagon.

The minimum degree of rotation by which this octagon can map onto itself.

For rotation we have to find the central angle of each side.

Complete angle = 360°

A regular octagon has 8 equal sides. All sides make same angle at center.

8Ф = 360°

Ф = 45°

If we rotate regular octagon by 45° then it map onto itself.

Hence, 45° correct answer.  

After 2 times clockwise rotation by 45° each time. We will get the image of A coincide with C as shown in attach figure.

C is second vertex of A.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

x=0

step-by-step explanation: