Find the 3 missing angles in the triangle - Geometry Triangle Practice Problem
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- Опубліковано 23 гру 2024
- How to solve for the angles in a triangle using algebra. Learn more math at TCMathAcademy.....
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2x + x + (x - 32°) = 180 so 4x = 180 + 32 = 212 -> x = 212 / 4 = 53°
Angle x is 53 degrees, angle 2x is 106 degrees and angle (x-32) is 21 degrees. Love your videos by the way ❤
Thank you
any triangle
every triangle
all triangles
have combined interior angle sum = 180°
Therefore, for this triangle:
x+2x+(x-32°) = 180°
4x - 32° = 180°
53degrees, 106degrees, 21degrees
This assumes a plane triangle. If it’s a spherical triangle the angles sum to greater than 180 degrees, so not any, every and all triangles.
@@eebinsv A triangle is a two-dimensional polygon defined by three line segments, known as sides, that connect three points called vertices. Each triangle has three interior angles, and the sum of these angles always equals 180 degrees. Triangles can be classified based on side lengths (equilateral, isosceles, scalene) and angle measures (acute, right, obtuse)
@@tomtke7351 They're being pedantic, but they're correct. On a hyperbolic plane (a saddle-back surface, like a Pringle) triangles have interior angles which add up to less than 180°. And on a spherical surface, they add up to more than 180°. (Think of a triangle on a globe, with the sides being from the north pole, down the Greenwich meridian to the equator, then along the equator to 90° east, then back up to the pole. That creates three right-angles.)
@dazartingstall6680 but, by definition, they're NOT triangles
x + 2x + x − 32 = 180
4x = 212
x = 53°
∴ 2x = 106°, x − 32 = 21°
_Check: 53 + 106 + 21 = 180_
Answer: The 3 angles :
X = 53 degrees
2X = 106 degrees
X - 32 = 21 degrees
-------
The sum of the 3 angles of a triangle = 180 degrees.
The sum of the 3 given angles = X+2X+X-32 degrees.
Therefore,
X+2X+X-32=180 deg.
4X-32=180 degrees
4X=180+32degrees
X= 212/4 = 53degrees.
2X = 53 * 2=106 deg.
X-32= 53-32= 21 deg.
53, 106, 21 just add all 3 to = 180 easy thanks for the fun.
Triangle Property : Angle Sum Theorem :
"The sum of the three interior angles of a triangle is always 180°"
x° + 2x° + x° - 32° = 180°
4x° = 180° + 32°
4x° = 212° 4x°/4 = 212°/4
x° = 53°
-------------------------------------
x° = 53°✅
2x° = 2 · 53° = 106°✅
(x - 32°) = 53°- 32° = 21°✅
53° + 106° + 21° = 180°
I love me a good algebra problem. Let’s begin.
There is one fact you must know to solve this problem. That fact is that in flat Euclidean space (such as a piece of paper laid flat), the sum of the measurements of the three angles of any triangle is 180 degrees. This is a triangle in flat Euclidean space, so we can set up our equation:
x + 2x + (x - 32) = 180
x + 2x + x - 32 = 180
Combine the x terms:
4x - 32 = 180
Add 32 to both sides:
4x = 212
Divide both sides by 4:
x = 53
So x is 53 degrees. Let’s make sure:
53 + 53*2 + (53-32)
53 + 106 + 21
180
There we go. Oh, and those are also the angle measures.
Someone need to explain how the parentheses in (x-32) are allowed to be ignored.
@imagseer Yeah, I wasn’t happy about that, but since I didn’t know what x was yet, you just have to get rid of them. It doesn’t affect the answer.
The sum of a triangles interior angles being 180 degrees is only true for plane triangles, a special case.
The default assumption at this level of education is that we're talking about Euclidean geometry.
What’s the name of triangle
All the angles and sides are of different sizes, so it's a scalene triangle.
Frederick
@@erniemorris9991 I was going to say Steve.
@@terry_willis That's its second name. Frederick Steven Percival Archibald Montague-Hatrack III. (Of the Sussex Hatracks. Ever since the infamous cream bun incident of 1798, we don't mention the Yorkshire branch in polite society.)
45,45 and 90.
It isn't 90 degrees.
@@helenaamaral4659 check the math again
Please
The angles are 53and 106.and 21 degree.