Perimeter of a kite

Please show your personal efforts.

What are the measures of the four angles in the middle of the kite?
 
Yes. Not the ones on the outside, the ones in the middle.

Hint: There is a Pythagorean Theorem in your future.
 
Alrighty. Run with that. Make some conclusions and some calculations.
 
Use the Pythagorean theorem for the top left triangle. Does that give you any information for that triangle and any others?
Do the same for the bottom left triangle as well.
 
Jomo said:
Use the Pythagorean theorem for the top left triangle. Does that give you any information for that triangle and any others?
Do the same for the bottom left triangle as well.
Click to expand...
3^2 + 4^2 = C^2. Is that correct?
 
I didn't check your arithmetic, but I did read the original problem statement. It wants "exact".
 
Jomo said:
Why are you stopping there? Find C. Same for your post before this one.
Click to expand...
3^2 + 4^2 = C^2
9 + 16 = C^2
C^2 = 25
Sqrt(25) = 5

3^2 + 9^2 = C^2
9 + 81 = C^2
C^2 = 90
Sqrt(90) = 9.48683298

P = 2 x 5 + 2 x 9.48683298
= 10 + 18.973666
= 28.973666
 
rachelmaddie said:
3^2 + 4^2 = C^2
9 + 16 = C^2
C^2 = 25
Sqrt(25) = 5

3^2 + 9^2 = C^2
9 + 81 = C^2
C^2 = 90
Sqrt(90) = 9.48683298

P = 2 x 5 + 2 x 9.48683298
= 10 + 18.973666
= 28.973666
Click to expand...
No approximations (unless your teacher insists on this)
sqrt(90) = sqrt(9*10) = sqrt(9)*sqrt(10) = 3sqrt(10)
P = 2*(5+3sqrt(10))
 
rachelmaddie said:
I don’t understand what you did here.
Click to expand...
I hope that you know that if \(\displaystyle a~\&~b\) are positive then \(\displaystyle \sqrt{ab}=\sqrt a\cdot\sqrt b~??\)
We know that \(\displaystyle UV=5~\&~XU=\sqrt{90}=\sqrt{9}\sqrt{10}=3\sqrt{10}\)
 
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