Have you tried this technique? | Find the angle X | (Two isosceles triangles in a right triangle!!!)

Рет қаралды 11,634

Жыл бұрын

Learn how to find the angle X in the given diagram. Two isosceles triangles in a right triangle. Solve this tricky geometry problem by using the isosceles triangle properties, Pythagorean Theorem, and Triangle sum theorem.
Today I will teach you basic tips and hacks to solve this tricky geometry problem in a simple and easy way. Step-by-step tutorial by PreMath.com
• Have you tried this te...
Need help with finding the angle X in this complex Geometry question ? You're in the right place!
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Have you tried this technique? | Find the angle X | (Two isosceles triangles in a right triangle!!!)
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Пікірлер: 60

@DDX01 Жыл бұрын

You made me math expert because you are my math guru.

@PreMath Жыл бұрын

Wow! Thank you! Cheers! 😀 You are awesome. Keep it up 👍

@DDX01 Жыл бұрын

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@DDX01 Жыл бұрын

I am really thankful to you

@robertakerman3570 Жыл бұрын

@@PreMath 10 Q!

@wackojacko3962 Жыл бұрын

My thinking is stronger because of the problems you present and I am becoming better at Math. Thank you! 🙂

@PreMath Жыл бұрын

You are very welcome! Thanks for your feedback! Cheers! 😀 You are awesome. Keep rocking 👍

@XDXD-om9rc Жыл бұрын

Same🙏

@rashidchatani Жыл бұрын

I focused on Quadrilateral CDEF and the Straight line AEB Angles in Quadrilateral = 360 90 + 180 - a + 180 - b + x = 360 Simplify: Eq1: x - a - b = - 90 Angles on straight line Eq2: x + a + b = 180 Add Eq1 + Eq2 2x = 90 Therefore x = 45

@PreMath Жыл бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@KAvi_YA666 Жыл бұрын

Thanks for video.Good luck sir!!!!!!!!!

@PreMath Жыл бұрын

Thank you too You are awesome. Keep it up 👍

@misterenter-iz7rz Жыл бұрын

Assume x is well determined, it suffices to consider some special case, that is AC=CB, AE=EB, thus x is clearly 45.

@PreMath Жыл бұрын

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@HappyFamilyOnline Жыл бұрын

Very well explained 👍 Thanks for sharing 😊

@PreMath Жыл бұрын

Thanks for liking

@ybodoN Жыл бұрын

Of course, we get to the same result if we start from x = 180° − (α + β). Then x = 180° − (½ (180° − y) + ½ (180° − z)) which gives x = ½ (y + z).

@PreMath Жыл бұрын

Thanks You are awesome. Keep it up 👍

@normanc918 Жыл бұрын

Yes, I did the same.

@joseeduardomachado3436 Жыл бұрын

Parece ser difícil mas é tranquilo. Gostei.

@PreMath Жыл бұрын

Obrigado pelo seu feedback! Saúde! 😀 Você é incrível. Continue assim 👍

@msafasharhan Жыл бұрын

Good explination Sir thankyou

@PreMath Жыл бұрын

Always welcome You are awesome. Keep it up 👍

@alster724 Жыл бұрын

Super easy although I have an alternate method 2a+y= 180° 2b+z= 180° Adding both equations, we get 2(a+b)+y+z= 360° But y+z= 90° 2(a+b)+90°= 360° (a+b)+45° = 180° (a+b)= 135° a,b, and x form a straight line a+x+b= 180° Since a+b= 135° x+135°= 180° x= 45°

@PreMath Жыл бұрын

Great!

@Ahmed-mn1ri Жыл бұрын

Beautiful question

@PreMath Жыл бұрын

Thanks dear You are awesome. Keep it up 👍

@luigipirandello5919 Жыл бұрын

Beautiful geométric question. Thank you.

@PreMath Жыл бұрын

Glad you liked it! You are awesome. Keep it up 👍

@williamwingo4740 Жыл бұрын

Got it by a slight variation of your method, even labeling angles y and z as you did. Your angle alpha = (180 -- y)/2 = 90 -- y/2; and beta = (180 -- z)/2; BUT z = (90 -- y), so beta = (180 -- (90 -- y))/2 = 90 -- 45 + y/2. x = 180 -- alpha -- beta, so x = 180 -- (90 -- y/2) -- (90 -- 45 + y/2) = 180 -- 90 + y/2 --90 + 45 -- y/2. The y/2 terms cancel and we have x = 180 -- 90 -- 90 +45 = 45 degrees. Cheers. 🤠

@PreMath Жыл бұрын

Nice work!

@williamwingo4740 Жыл бұрын

@@PreMath hardest part is getting all the signs and parentheses right....

@Copernicusfreud Жыл бұрын

Yay! I solved it.

@PreMath Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@devondevon4366 Жыл бұрын

45 Let's label the green isosceles P, S, S Let's label the yellow isosceles M, M, and R, then P + R =90 equation 1 P + 2S =180 2M + R =180 ; hence 2P + 2R + 2S + 2M = 450 (add all three equations) 2(P + R + S + M) = 450 (factor out 2) P+ R + S + M =225 (divide both sides by 2) equation 6 90 + S + M = 225 ; hence (substitute the value of P+R into equation 6) S + M = 225-90 S+M =135 but S+M+X =180 (since a straight angle is 180 degrees); hence 135 + X = 180 degrees; HENCE X= 180-135 X =45 Answer

@PreMath Жыл бұрын

Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

@vkr122 Жыл бұрын

Skaitam kopā:x+y+2a+2b=360 2(a+b)=270 a+b=135 x=45.

@PreMath Жыл бұрын

Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

@santiagoarosam430 Жыл бұрын

Respetando las premisas iniciales del problema, podemos decir: AC=CB y E=punto medio de AB → Ángulos A=B=45º → Ángulo E=180º=[2(180º-45º)/2]+X → X=180º-135º=45º Gracias y un saludo cordial.

@PreMath Жыл бұрын

Thanks dear You are awesome. Keep it up 👍

@misterenter-iz7rz Жыл бұрын

A+B=90, angle DEA+BEF=90-A/2+90-B/2=180-(A+B)/2=180-45, thus x=45.😊

@PreMath Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@FreestyleViewer Жыл бұрын

Simplest Method is This: We observe that in any Right-Angled Triangle we can always take a point E and form two Isosceles Triangles like these. That means in all the cases the value of x is Fixed. Therefore, we can assume any values of the Angles of any Isosceles Triangle and find the x. For Example: Assume one Angle 30°, the other one will become 60°. Hence, x will be- 180° - (150/2+120/2) = 45° Furthermore, If we use the “Law of Monotonicity of the Relationship in Geometrical Figures”, we can even assume one angle 0°, the other one will become 90°. Hence, x will be- 180° - (180/2+90/2) = 45° This is how here in India the Multiple Choice Questions are solved in Competitive Examinations.

@JLvatron Жыл бұрын

I gat it!

@PreMath Жыл бұрын

Super! You are awesome. Keep it up 👍

@gelbkehlchen 11 ай бұрын

Solution: angle CAB = α, angle CBA = β, α+β = 90°, angle DEA = (180°-α)/2 = 90°-α/2 [because of the isosceles triangle], angle BEF = (180°-β)/2 = 90°-β/2 [because of the isosceles triangle], x = 180°-(90°-α/2)-(90°-β/2) = 180°-90°+α/2-90°+β/2 = (α+β)/2 = 90°/2 = 45°

@AnonimityAssured Жыл бұрын

Ah, excellent, a minimal-information problem, which offers us a shortcut to the solution. Spoiler alert. Without loss of generality, we can safely assume symmetry as a special case, so that the angles at points A and B are each 45°, or 180° / 4. Therefore, the sum of angles AED and BEF is 180° ∙ 3 / 4, so that angle x is 180° / 4 = 45°.

@PreMath Жыл бұрын

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

@danieldennis9831 Жыл бұрын

∠A=a ∠B=b ∠C=c a+b+c=180 c=90 conclusion: a+b=90 (eq1) |AD=|AE conclusion ∠AED=∠ADE=f |BE=|BF conclusion ∠BEF=∠BFE=g Using rules of triangles conclusions: a+b+c=180° c=90° (eq1) a+b=90 (eq2) f+g+x=180° 2f+a=180° (eq3) a=180°-2f 2g+b=180° (eq4) b=180°-2g x+f+g=180° (eq5)x=180°-(f+g) Substition and simplification concludes ANSWER: x=45°

@PreMath Жыл бұрын

Super! You are awesome. Keep it up 👍