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Geometry 64 Online
OpenStudy (anonymous):

Can anyone explain why I got this wrong? For questions 1 and 2, use the diagram below. 1. The figure above is a regular octagon with radii and an apothem drawn. What is the measure of angle 1? A. 22.5 degrees B. 45 degrees C. 60 degrees D. 67.5 degrees 2. What is the measure of angle 2? A. 22.5 degrees B. 45 degrees C. 60 degrees D. 67 degrees I chose 60 degrees for question 1 and 60 degrees for question 2. I thought angle 1 was 60 because the apothem makes a 30-60-90 triangle, so the top angle must be 30, double that to get 60, then all top angles around the octagon are 60.

OpenStudy (anonymous):

and then for question 2, I again was thinking it was a 30-60-90 triangle, and if the top angle is halved, it's 30, and since it's a right triangle, the other is 90, so the last must be 60, but i was still wrong, can anyone explain why? Here's the octagon:

OpenStudy (amistre64):

why did you chose 60?

OpenStudy (anonymous):

For which one? Question 1? I chose it because I thought, since the apothem makes a 30-60-90 triangle, then the top angle is doubled to get 60, so all the top angles around the octagon should be 60.

OpenStudy (amistre64):

... it doesnt make a 30-60-90

OpenStudy (amistre64):

think of it this way ... can we fit a circle around the octagon?

OpenStudy (anonymous):

well, depends on the size of the circle.

OpenStudy (amistre64):

a circle ... is generic so it as long as A circle fits ...

OpenStudy (anonymous):

You lost me, lol

OpenStudy (amistre64):

fit a circle around the octagon ... now imagine that you have a pizza, how many slices of pizza does it make?

OpenStudy (anonymous):

8.

OpenStudy (amistre64):

good, now we know the degree of the pizza in total is 360, how many degrees is 1/8 of it?

OpenStudy (anonymous):

\[\frac{ 360 }{ 8 } = 45?\]

OpenStudy (amistre64):

yep ...

OpenStudy (amistre64):

what is 45 * 8?

OpenStudy (anonymous):

360. I get it now :) Thanks!

OpenStudy (anonymous):

And for question 2, it would be 45 + 90 + x = 180 x = 45

OpenStudy (amistre64):

now for angle 2 ... we know that the central angle is 45 ... and we have an iso tri ..|dw:1398345559877:dw| by properties of a triangle, that angles add to 180 \[\alpha+\beta+\beta=180\] solve for \(\beta\)

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