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December 6th, 2010, 08:45 AM   #1
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X,Y angles.

[color=#000000]Find the measure of the angles X and Y.
[/color]

[attachment=0:1m0lk1hg]angles.png[/attachment:1m0lk1hg]


[color=#000000]Where ? put Y .[/color]
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December 7th, 2010, 02:43 PM   #2
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Re: X,Y angles.

Hello ZardoZ,

I'm not sure on how to phrase in English, but I'll try:

First we'll solve for X:
The angles of the Pentagon are .
constructing an isosceles triangle with top angle of gives a base angle of
(The "baseline" is the lengthened line from M to . Now by using complementary angles, we have:

Now for Y.
Lengthen the line to the other pentagon intersecting the triangle in . Now, we have a triangle, B. So we have
The angles of a hexagon are

Angle M = Angle B (do you see that in the picture?)
So Angle B =

Now, angle Y

Hoempa
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December 7th, 2010, 03:17 PM   #3
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With "in ." changed to "in B." (which you probably intended) both calculations make sense and get the correct answers. The minimal annotation of the diagram makes it a bit awkward to explain things clearly. In particular, one needs to assume that the pentagons and hexagon are regular, so that their angles are known.
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December 7th, 2010, 06:10 PM   #4
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Re: X,Y angles.

[color=#000000]The answers are correct, I must have mentioned though that the pentagons and hexagon are regular.[/color]
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December 7th, 2010, 07:58 PM   #5
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Re: X,Y angles.

Quote:
Originally Posted by Hoempa
Hello ZardoZ,

I'm not sure on how to phrase in English, but I'll try:

First we'll solve for X:
The angles of the Pentagon are .
constructing an isosceles triangle with top angle of gives a base angle of
(The "baseline" is the lengthened line from M to . Now by using complementary angles, we have:

Now for Y.
Lengthen the line to the other pentagon intersecting the triangle in . Now, we have a triangle, B. So we have
The angles of a hexagon are

Angle M = Angle B (do you see that in the picture?)
So Angle B =

Now, angle Y

Hoempa
how come (180-36)/2=144 and (180-120)/2=60 ( doesnt "/2" mean divide by two or am i missing something?)
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December 7th, 2010, 08:59 PM   #6
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I think Hoempa simply forgot to omit "/2", which doesn't belong in that line, but was needed in the earlier calculation.
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December 8th, 2010, 12:46 PM   #7
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Re: X,Y angles.

What you say is correct, skipjack, I copy-pasted these calculations and forgot to eliminate "/2", and I see that I was to say "in B." I can't edit though. Glad, it made sense, afterwards.

Hoempa
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