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Alja [10]
4 years ago
6

Please help me this is my second to last question

Mathematics
1 answer:
Kamila [148]4 years ago
6 0

Answer:the answer is B

Step-by-step explanation:

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Step-by-step explanation:

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Need help .... Regular octagon ABCDEFGH rotates 360 degree clockwise about it's center . After how many 45 increments will A' (
oksian1 [2.3K]

Answer:

If the octagon is clockwise, then after 5 times 45 increments A' will coincide with F.

If the octagon is counterclockwise, then after 3 times 45 increments A' will coincide with F.

Step-by-step explanation:

Case 1: Let the octagon is clockwise

It is given that a regular octagon ABCDEFGH rotates 360 degree clockwise about it's center.

There are 8 vertices and the central angle between two consecutive vertices is 45 degrees.

Central angle between AB is 45 degree.

Central angle between AC is

\text{Angle between AB}+\text{Angle between BC}=45^{\circ}+45^{\circ}=2\times 45^{\circ}

Central angle between AD is

\text{Angle between AB}+\text{Angle between BC}+\text{Angle between CD}=45^{\circ}+45^{\circ}+45^{\circ}=3\times 45^{\circ}

Similarly,

Central angle between AE is

4\times 45^{\circ}

Central angle between FA is

5\times 45^{\circ}

Therefore after 5 times 45 increments A' will coincide with F.

Case 2: Let the octagon is counterclockwise

FA=AH+HG+GF

FA=45^{\circ}+45^{\circ}+45^{\circ}

FA=135^{\circ}

FA=3\times 45^{\circ}

Therefore after 3 times 45 increments A' will coincide with F.

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