Find the angle X and justify | Learn how to Solve this Tricky Geometry problem Quickly

Learn how to find the angle X in the given diagram. Solve this tricky geometry problem by using Exterior angle Theorem and alternate interior angles Theorem.

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Find the angle X and justify | Learn how to Solve this Tricky Geometry problem Quickly

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Olympiad Mathematics
pre math
Po Shen Loh
Learn how to find the angle X
How to Solve this Tricky Geometry problem Quickly
Exterior Angle Theorem
Alternate interior angles
premath
premaths

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[ahmadalhelo]

You can use the exterior angle theorm in the triangular ABC to prove that b=a+23 then b-a=23

[xof-woodworkinghobbyist]

Interesting.
Could you not use the Exterior angle theorem on ABC? Beta = Alpha + 23
Then you can resolve for x with this equation and your equation 1.
Great video, great problem. Thanks!

[normanc]

Thank you sir for video. We can use Exterior Angle Theorem for both triangles ABC & ABD, then b = 23 + a (1)
2b = X + 2a
Multiple 2 to (1) we get 2b = 46 + 2a then obviously by naked eyes that X = 46.

[rivivuel]

Awesome! It can also be done this way!

These are the equations

1. b=23+a
2. 2b=X+2a

Substitute

2(23+a)=X+2a
46+2a=X+2a
46+2a-2a=X+2a-2a
46=X
X=46

[MohammadSami-ul-lah]

Sir we solve this question by exterior angle property but thanks to you for teaching us it in a unique way.Sir i always like your videos.
Stay blessed, from Kashmir India.

[tks]

There is an easier method for this question.
B=a+23°
2B=2a+x
2(a+23°)=2a+x
2a+46°=2a+x
x=46°

[devindermehta]

Instead of drawing a parallel line can use exterior angle theorem for 2nd triangle also

[mehulpunia]

This problem is given to 9th standard students in India
I solved it in my 9th class by using exterior angle property

[quyinh]

Àter minute 2:45. No need to draw the FP line. Considering the exterior angle of triangle BCA, we have CBE = CAB+BAC ----> beta = alpha + 23

[yamunaravi]

I got this answer by using exterior angle and sum of angle in triangle is 180. And sum of angles 180 in straight line

[mathejogi]

Right triangle: 2a+x=2b;
x=2b-2a
Left triangle: y+a=b (in this case y=23).
We have x=2(y+a)-2a=2y=46

[soniamariadasilveira]

Obrigada por explicações tão claras e torna tudo mais fácil para resolver este desafio matemático!

[satrajitghosh]

exterior angle CBE
= beta = 23° + alpha
again exterior angle DBE
= 2 beta = x + 2alpha
Hereby x = 2 ( beta - alpha) = 2*23°
= 46°

[msafasharhan]

،Hello Sir, we can say B=23+Alfa insted plotting parallel line

[philipkudrna]

I arrived at x=46 and I am pretty confident, that this is correct, but my approach was rather „messy“. Now I am curious, what the more elegant solution looks like and I watch the video…
Yes, the traversal trick made it much easier. I fuzzed around with two more angles that I ultimately had to get rid off again. This is much easier and actually pretty intuitive. I had to solve several equations to derive that beta=alpha+23… 😂

[APUS_NUNN]

Danke für diese richtig schöne Aufgabe und die tolle Lösung. 👍

[bigm]

Another lovely little problem. Thanks professor.

[devondevon]

x =46 answer
let alpha = A, beta= B
Starting with the triangle, ABC since angle C=23 and angle A= alpha then angle CBE = 23 + alpha,
hence beta= 23 + alpha; hence B= 23 + A; therefore
2B =46 + 2A; hence angle ABD = 180-46 + 2A = 134-2A;
let's label the point of intersection between line B and D "P" to form the triangle A B P
hence two angles in triangle ABP are 134-2A, A, or a total of 134-A; hence angle
APD = 134-A; hence
134- A + A + x =180
134 + x =180
x =180-134
x=46 Answer

[montynorth]

Triangle ABC.
Alpha + 23 = Beta.
Alpha and Beta are not fixed values, only their relationship to each other.
Let Beta = 60 degrees.
Then Alpha = 37 degrees.
Triangle ABD.
X + 2 Alpha = 2 Beta.
X = 2 Beta -- 2 Alpha.
X = 120 --74 = 46.

[aaravtiwari]

We can also do this by assuming the line bisect the side of triangle 90 degree