Can You Find Angle X? | Quick & Simple Explanation

[stephenbrand]

A nice problem for Christmas Eve. Thankyou and best wishes to all PreMath problem solvers.

[crp]

In your mind's eye, gradually move the point B until it overlaps C, dragging along all lines leading to B onto C. You are allowed to do this, because the only requirement is that you keep the angle pairs at B and A equal.
Once you do this, you'll see that the ABD triangle now has a right angle at A (as you are splitting 180 degrees in two) and a 34 degree angle at B (as you are dividing 180-112 in two). The angle D is now clearly 180-90-34 (sum of angles of triangle ABD). Can get 56 without much effort.
Takeaway: always note what is fixed and what is malleable, and change what you can to simplify as needed.
Cheers!

[predator]

Fantastic solution for this nice quation 👍😊. Thank you teacher 🙏.

[silviatotaro]

Very nice problem! Merry Christmas from Italy!

[Aditya_Senpai]

3:10 In my opinion instead of using exterior angle theroem and writing too long, we can do it in this method:-

Angle ACB=180°- 112°
Angle ACB= 68°
So, sum of Angle CBA and Angle CAB will be 180°-68°=124°
So, Beta+Alpha= 124°

So, Alpha+Beta+x=180
124+x=180
x=180-124
x=56
Done!

[paulc]

Thank you for the video. Before watching I had worked out X = 56.
2 x A + 2 x B + 112 = 360.
A + B = 124, so X = 180 - 124 = 56.

[pixcalibur]

Let a = congruent angles on line A and b = congruent angles on line B. Then we have 2a+2b+angle BAC+angle ABC = 360 (2 lines x 180 degrees each)
angle BCA = 68, which then gives sum of angle BAC + angle ABC = 112
Thus, 2a+2b+112=360 -> 2a+2b=248 -> a+b=124, which is the sum of the other 2 sides of the triangle.
Then X = 180-124 = 56 degrees

[spafon]

Nice easy one for us. The interesting thing about this problem is that there doesn't seem to be a single solution for alpha and beta but that's OK since all we need to know is alpha+beta and that provides the solution for x.

[math]

sure can, thanks for the challenge, merry Christmas

[johnryder]

Happy Christmas Premath and a Happy New Year hopefully enjoying your good content

[.]

Merry Christmas sir loads of love from India :)

[dautaytvedu]

Thank you for sharing the great video 👍

[Blacksquareable]

I'm so enjoying this - it's really putting the fun into maths.

[ALEX_FROM_E]

Приветствую. Спасибо за очередную задачу. Ты классный!

[carlyet]

X is half of 112 degrees. The cord cutting the angle is free so construct the symmetric case. Then x = 180 - 2a & 112/2 as 112 = (180-2a) + (180-2b) as b->a

[tombufford]

At a quick glance: Denoting the two equal pairs of angles, a and b. Then Triangle ABC angles sum = 180- (2 * a) + (180 - 2*b) + (180-112) =180. Then 2*a + 2*b = 248 and 180= a + b+ x. Then a+ b = 124. Then x = 180-124 = 56. Angle x = 56 degrees

[zplusacademy]

One more interesting figurative question ❓❤️🙏🙏

[abhishekpatil]

Let the two sets of congruent angles be labeled A and B respectively.
Now in triangle ABC Angle BAC + AngleABC+ AngleBCA=180 degrees. :Eqn (1)
But AngleBCA=180-112 =68 degrees.
Also Angle BAC= 180-2A and Angle ABC=180- 2B.
Substituting these values in eqn 1 we get,

180-2A+180-2B+68= 180.
i.e 2A+2B=180+68.
Dividing by 2 throughout we get,
A +B =124.
So Angle X =180-(A+B)=180-124 = 56 degrees.

[ΚΑΝΑΒΟΣΜΑΝΩΛΗΣ]

I hate calculations..but took me 18 secs...Thanks once more

[sameerqureshi-khcc]

Pakistan has sent flowers for you sir 😊🇵🇰🌹🌹🌹🌹