Urgently need help! ( 8th grade maths )

B

breadforl

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May 26, 2020
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image.jpg According to a friend, these are the steps:
180- { [180-(360-100)/2]/2+[(180-100)/2]*2 }

Question) Why divide by 2? Why/how are the divided triangles in AYC isosceles? Is there a formula/reference/way to prove that triangle ACX and AXY are indeed isosceles?

I just can't understand why we have to divide it by 2... I have spent about 2 hours on this question and I desperately need help.
P.S. Asked my class gc and the friend I got the steps from but no one gave me a concise answer
 
breadforl said:
View attachment 19221 According to a friend, these are the steps:
180- { [180-(360-100)/2]/2+[(180-100)/2]*2 }

Question) Why divide by 2? Why/how are the divided triangles in AYC isosceles? Is there a formula/reference/way to prove that triangle ACX and AXY are indeed isosceles?

I just can't understand why we have to divide it by 2... I have spent about 2 hours on this question and I desperately need help.
P.S. Asked my class gc and the friend I got the steps from but no one gave me a concise answer
Click to expand...
Are the rays AB and CD parallel?

1590489912989.png
 
breadforl said:
View attachment 19221 According to a friend, these are the steps:
180- { [180-(360-100)/2]/2+[(180-100)/2]*2 }

Question) Why divide by 2? Why/how are the divided triangles in AYC isosceles? Is there a formula/reference/way to prove that triangle ACX and AXY are indeed isosceles?

I just can't understand why we have to divide it by 2... I have spent about 2 hours on this question and I desperately need help.
P.S. Asked my class gc and the friend I got the steps from but no one gave me a concise answer
Click to expand...
I would never write it the way your friend did here!

I would take it in steps. One way is to draw in a line through X parallel to AB and CD, and label the left end Z. Answer these questions:

What is angle ZXA?
What is angle BAX?
What is angle BAY?
What is angle AYZ? (if you see that the line you drew passes through both X and Y; otherwise, just draw a parallel through Y)
What are the corresponding angles in the bottom half of the figure?
What is AYC?

Don't worry about the isosceles triangles too much; you don't need them. But when you answer my questions about the bottom half, you may see the reason.
 
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