TWO Methods to find the angle X | Learn how to Solve this Geometry problem Quickly
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- Опубліковано 11 вер 2024
- Learn how to find the angle X in the given diagram. Solve this tricky geometry problem by using the alternate interior angles 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
• TWO Methods to find t...
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TWO Methods to find the angle X | Learn how to Solve this Geometry problem Quickly
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A prodigious accomplishment. Thanks Professor!
Many thanks!
Glad you think so!
You are awesome. Keep it up 👍
Love and prayers from the USA! 😀
@@PreMath 👍🥂
A third method would be to construct a line at the bottom perpendicular to the two parallel lines making irregular heptagon.Then remembering the total angle of a heptagon 900, it's easy to arrive at the same answer of 52. Your methods are cool though. Thanks for keeping us active!!
Thanks for sharing! Cheers!
You are awesome. Keep it up 👍
Love and prayers from the USA! 😀
Sum of the interior angles of n-sided polygon is (n-2)*180.
By connecting the two parallel lines at the bottom we get 7-sided polygon.
Hence x+848 = (7-2)*180=900
X = 52
There is a 4th method, which I find easier.
Rotate the figure sidewards or 90° then draw angle bisectors then use different angle properties for parallel lines and the basic ones including the linear pair. Got the same answer of 52°
Awesomely. Gratitude to u.
Sorry, i don't speak english.
De hecho, tu método es lo que justifica el segundo método. Ya que la razón por la que los ángulos de abajo suman lo mismo que los de arriba, es que a esas dos sumas hay que añadirle lo mismo(dos ángulos de 90) para que den 900, ya que se pueden formar heptágonos arriba y abajo, y por eso esas sumas coinciden 😊
The top/bottom method is really nice! 👍
I found another way to calculate angle x, which is in some way related to the top/bottom method:
x = the absolute value of the alternating sum of the given angles.
x = |+70° - 104° + 92° - 110°| = 52°
or
x = |-70° + 104° - 92° + 110°| = 52°
I extended the line segment making the 92 degree and 110 degree angle to the left and right vertical lines, and used supplementary angles to make a quadrilateral on the left with angles of 110, 104, 88, and 58. Then a triangle on the right vertical line with the angles 70 and 58. Remaining angle x is 52.
I like it that you vary tough math problems and easy ones . Keep it up , Sir . Greetings from Germany . 👍
Thank you very much!
Glad you think so!
You are awesome, Claudia. Keep it up 👍
Love and prayers from the USA! 😀
Nice
Glad to hear that!
Thanks for your feedback! Cheers!
You are awesome. Keep it up 👍
Love and prayers from the USA! 😀
I appreciate the way you repeat the steps. Though some of the theorems presented are highly repetitive your restating them teaches the importance of constructing a methodology, so keep it up!
Hi Prof. PreMath,
I found this a rather fascinating problem. I had already intuited the use of the first solution with the alternate interior angles. But the second method esp. intrigued me as I'm new to the principle.
Easy enough to remember but I'm still perplexed by the logic of it. Any recommendations, given your list of links, as to where I can see these angle / triangle relations here spelled out so I can logically see why the sum of the bottom angles equals the sum of those at the top?
Enjoyed the video! Thx!
Draw a straight line from the 70° to the X. Pretend this is a diameter of a circle and the blue lines are how you cut the circle in half. Both halves are jagged and inconsistent, but they complement the other. They both are equal to a 1/2 of the whole circle!
The sum of the top angles equal the top 1/2 of circle, and the sum of the bottom angles equal the bottom half. Hope this helps!
@@valentinocaine2294
Hi Valentino,
Appreciate the reply and the willingnes to help me out.. But I must confess, I do not understand the argument or even the diagramming here being put forth. I screenshot the Premath image into a PowerPoint and drew the line from the 70 degree angle to the "X" angle and I do not get how the blue lines represent complementary halves of a circle, let alone how they can cut the circle into halves as none of them are 1/2 the diameter (= the radius).
For my drawn line I have a little tiny center triangle jutting up above (the 92 degree angle--the line cutting through the number 92) and all the rest falling below. I'm not seeing the symmetry (in fact it looks radically asymmetrical to me). And so, I'm not seeing the logic of how the upper triangles equal the total angles of the bottom triangles.
Again, I appreciate the help, but there's something I'm not getting.
@@sail2byzantium Im sorry, I sometimes don't explain things the best.
Get a piece of paper and draw a center line across. Now fold it on that line.
Unfold it flat and cut a continuous line similar to the blue line illustrated in the problem. Starting on the left point of the centerline, and ending on the right point of the centerline.
You'll have two pieces, top and bottom. Now fold the top half over onto the bottom half like you did earlier. You will see that all angles are mirrored in respect to your center line you drew. (Don't forget to look at the back.)
In other words the sum of the top angles equal the sum of the bottom angles.
Let me know if makes sense! Good luck
I used the first method to solve it. After seeing your demo I find the 2nd method is better and faster.
Very well explained👍
Thanks for sharing😊😊
can it be solved by extending 70 degree line to last parallel line and then extending x degree line forming a triangle at the end of angle x and a quadrilateral at the centre ?
Very well presented.
Both solutions are elegant, but I favor the 2nd solution method!
There is a 4th method (there is a third one in a separate comment) is to rotate the figure sidewards or 90 degrees then draw some bisectors and use angle theorems for parallel lines as well as basic angle properties such as the linear pair postulate etc.
Cheers from the Philippines
Congratulations 👏 Master 🇧🇷
Well done Sir
Why the sum of angles on the top is equal to the sum on the bottom ? can you explain please .
The alternate interior angles cancel each other out (70 & 70, 34 & 34, 58 & 58, 52 & 52) .
Stop the video where the vertical lines are drawn.
Each angle has its exactly equal counter angle at the next vertical line.
Thus the sum of the angles above is exactly equal to the sum of the angles below.
@@Waldlaeufer70 ok i understand now . thx
@@ludosmets2018 ok thx
@@ludosmets2018 ok thx
I like the second method since it does not require drawing in any extra lines it just uses the angles you can see from the original diagram
Sort of did this in my head using a variant of your second method. Taking downward angles as negative, and upward angles as positive, the sum of the angles is zero. So -70+104-92+110-x=0. x=110-92+104-70. x=52.
Thank you ❤️
maza a gya 🥰
Bello e interessante soprattutto il secondo metodo professore.
Grazie
thnx
There is another way:
First, construct a line joining the two parallel sides of the diagram, perpendicular to the sides, and above all the 4 other line segments (below works just as well). We now have an irregular seven-sided polygon. The formula for the sum of the interior angles of a polygon is (n-2)*180, where n is the number of sides; for a seven-sided polygon the sum is 900 deg.
From our modified diagram, we know, or can easily determine, 6 of the interior angles, and the sum of those 6 is 772 deg. The remaining angle (call it alpha) is therefore 900 - 772 = 128.
Since x and alpha are supplementary angles (sum is 180), then x = 180 - alpha = 180 - 128 = 52.
Just as easy as the other two methods.
Thanks for video.Good luck sir!!!!!!!!!!!!
Thank you too
You are awesome. Keep it up 👍
Love and prayers from the USA! 😀
Ans : 52 degree
you only said the diagram is not upto scale.
where in question it has been given that lines are parallel?
Dear Sir, extend the lines of 70 degree and also angle X, both will coincide and we will get a quadrilateral, the total angle will be 360 degree, find out the angles of the parallelogram and use 180 degree - angles to find all the angles of 70 degree triangle and you will get the x using alternate angle theorem.
@@rainerinedinburgh5807 sorry was distracted, it's a quadrilateral
@@rainerinedinburgh5807 was speaking with a person. When I was just looked back I was like omg I made a mistake, it's quadrilateral and I wrote parallelogram.
@@rainerinedinburgh5807 100% what you said is right. Thats what I wanted to say.
I guess I assumed that the parallel lines were 90° but I simply pretended a 90° horizontal line shot right. This would make a triangle on the left a right triangle. 70+90=160. 180°-160=20°
Just repeat the process keeping in mind that the sum of the interior angles of a triangle is 180° and a horizontal line is 180°. A little more work but I got the same answer.
My method is a bit more convoluted unfortunately
1. I extended the line that had the x degree angle till it reached the first line
2. Then i extended the line that made 70 degree angle with the first line, thus creating a quadrilateral.
3. Using 104 and 110 degree angles, we can calculate their complementary angles for the interior angles of the quadrilateral: 76 degree and 70 degree respectively
4. We have 3 of the 4 interior angles of the quadrilateral (92, 76, 70), thus we can calculate the 4th angle (360 - (92 + 76 + 70) = 122
5. The extension of the two lines also makes a triangle with one of the sides lying on the first line. The 122 degree acts as exterior angle, therefore the sum of the two opp. angles is 122
6. Since we know one of the angles is 70 degree, therefore second angle must be 52 degrees
7. X = 52 since the 52 degree angle and x are alternate interior angles
Top banana 👍🏻
52. 214-162=52.
Lo del segundo método no lo sabía.
I've just looked at the thumbnail. I believe the answer to be 62°.
My reasoning:
(110+104)-(92+70)=x
Feel free to berate me if I got it wrong.
Tirando la parallela per il 92 e prolungando i lati che formano gli angoli 70 e X ottengo un quadrilatero la cui somma di angoli dà 360...quindi 76+92+70+(70+X)=360...X=52
I built a triangle were 92 is.
I klik on like Button in all of yors videos evry and each time. They all are amazing with your amazing explanations.
Thank you very much teacher. 👍✌️🍁🌸
So nice of you, dear
Thanks for your continued love and support!
You are awesome. Keep it up 👍
Love and prayers from the USA! 😀