Question

@satellite73

Answer 1

you rang?

Answer 2

ring ring

Answer 3

the answer is 36, 36 but how?

Answer 4

72? ok

Answer 5

^that can't be right @satellite73

Answer 6

that is wrong, scratch that!

Answer 7

exterior angle?

Answer 8

@agent0smith has it, i am way off base

Answer 9

internal angles are 108
half of that is 54
i can't draw a damned picture, but you have a right triangle with one angle 54, right angle 90. remaining angle has to be whatever adds up to 180, namely 36

Answer 10

hard without draw tool and latex

Answer 11

maybe @agent0smith has a better explanation, or a picture

Answer 12

here is an actual picture
http://www.americanbookcompany.com/newsite/samplebooks/SAMPLE%20PAGES%20-%20Passing%20the%20Minnesota%206th%20Grade%20MCA%20III%20in%20Mathematics/files/assets/seo/page19.html

Answer 13

You can use the isosceles triangles with the 108 degree angles to find x... but yeah.. hard to explain w/o a pic.

Answer 14

ABCDE is a regular pentagon (given), so each interior angle is


I = 180(n-2)/n


I = 180(5-2)/5


I = 108


That means angle EAB = 108 degrees. Similarly, angle EDC = 108 degrees (all 5 interior angles of this pentagon are 108 degrees)


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Triangle EAB is an isosceles triangle because AB = AE. Regular polygons have all sides congruent. Since the legs are congruent, the base angles are congruent.


So we know that


angle AEB = angle ABE


They are both x degrees at the moment. The three angles add to 180 degrees


x + x + 108 = 180


2x + 108 = 180


2x = 180 - 108


2x = 72


x = 72/2


x = 36


So,


angle AEB = 36 degrees


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These similar steps can be used to show that


angle CED = 36 degrees


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Now use the angle addition postulate to get


angle AEB + angle BEC + angle CED = angle AED


36 + y + 36 = 108


y + 72 = 108


y = 108 - 72


y = 36