Isosceles Triangles Inside a Right Triangle | Daily Math Geometry

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sum angles on the diagonal line : a+b+x=180 ;
sum angles on the 4 sides figure : (180-a)+(180-b)+x+90 =360
(a+b)=180-x ; x+90-(a+b)=0
x+90+x-180 = 0
2x = 90 ; x = 45 degrés

tontonbeber
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I observed that Triangle BDE was an equilateral Triangle so all angles are 60 (I know, I know, you shouldn't assume but if it isn't an equilateral triangle, its pretty close). That would mean angle C would be 30 since 180 - A(90)- B(60) = C(30). That would make angles F and E2 75 each. So then X=180 - E1(60) - E2(75)=45

shakeandbake
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thank you, I'd like smth like that every day

tim_despair
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I always try to solve these kind of tasks in my mind. 'Cause you only have to realize this task could be true to any right triangles. So just give random value to alpha&beta (of course alpha+beta=90°) Since we have the value there are several solving method to choose.

mikemanh
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Loving your application you use for writing board?

mathme
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It is interesting that the answer is always 45 degrees. That is, it doesn't depend on the sizes of the other angles in the right triangle. The orientation, but not the size, of angle _x_ depends on the sizes of the other angles.

artsmith
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ADEF: X = 360-90-D-F=270-D-F; F=180-(180-C)/2=90+C/2; D=90+B/2=90+(90-C)/2=135-C/2; X= Done!

towalks
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x
= π - (π/2 - alpha/2) - (π/2 - beta/2)
= (alpha +.beta)/2 = π/2

satrajitghosh
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Nice one. What a pity i wasn't patient enough to find it by myself.

mamiesimone