You are assuming that angle 7x is either acute or obtuse. We are told that the diagram may not be 100% true to the scale. We are not told that an angle being obtuse in the diagram means that it will be obtuse in the solution. Your solution is correct if 7x is obtuse. However, what if 7x is greater than 180° but less than 360°? When you connect the bottom apexes, the vertex of 7x will be below that line. If you don't make math errors, you will find the correct value of x.
RUSSIA! Сумма углов в треугольнике 180 градусов, в четырёхугольнике 360 градусов, в пятиугольнике 540 градусов, и т. д. Преобразуем пятиугольник в четырёхугольник, для этогосоединим прямой линией углы 2х и 3х, к полученной сумме углов добавим разницу 180-7х и приравняем это к 360 градусам: 2х+6х+5х+3х+180-7х=360; 9х=180, откуда х=180/9=20 градусов.
The internal angles of a polygon sum to (n-2)180°, where n is the number of sides of the polygon. As this is a pentagon, the internal angles sum to (5-2)180° = 540°. 2x + 6x + 5x + 3x + (360°-7x) = 540° 16x + 360° - 7x = 540° 9x = 540° - 360° = 180° x = 180°/9 = 20°
We may join vertices of angle 2x degrees and 3x degrees Then a quadrilateral will be formed. Then for this quadrilateral the sum of angles is 6x +2x +3x +5x + 180 -7x = 360 > 9x =360 -180=180 > x =20 Hence x = 20 degrees
@ 1:33 All of my polygons have an infinite number of sides and I cannot tell the difference between any of em! This five sider made life a little easier for me today. 😊
My way of solution is ▶ The interior sum of the angles of a Polygon (Pentagon): n= 5 s(A)= (5-2)*180 s(A)= 540° s(A)= 6x+5x+3x+2x+(360°- 7x) 540°= 16x-7x+360° 180°= 9x x= 20°
The sum of angles within a polygon is (# sides - 2)*180. So, for a five sided polygon that sum is: 540 (180*3), which should be equal to: 2x + 6x + 5x + 3x +(360-7x). Solving for x = 20.
Let's find x: . .. ... .... ..... The interior angle sum for a polygon with n corners is given by: (n − 2)*180° Here we have five corners and five interior angles: 6x + 5x + 3x + (360° − 7x) + 2x = (5 − 2)*180° 9x + 360° = 540° 9x = 180° ⇒ x = 20° Best regards from Germany
I couldn't remember that angle formula for polygons, but I know 4 angles is 360, so I drew a line from the back of the 7x angle to the perpendicular of the top line (between 5x and 6x), giving 2 4-sided shapes, assigning A and B to the resultant interior angles, where (A+B=360-7x): A+90+6x+2x=360 B+90+5x+3×=360 Add both lines: (A+B)+180+16×=720 Substitute: (360-7x)+180+16x=720 -540 both sides 9x=180 ×=20
Solution: This pentagon can be divided into 3 triangles, so the sum of the angles in this pentagon is 3*180° = 540°. This means: 2x+360°-7x+3x+5x+6x = 540° |-360° ⟹ 9x = 180° |/9 ⟹ x = 20°
Woww, after watch many your videos, my skill improves. And, i can answer it before you giv3 the solve. Thanks teacher☆
I'm glad you're enjoying the videos and making progress! 😊
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Thanks Sir
Thanks PreMath
We are learning more and more from your exercises.
Good luck with glades
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Connect two bottom apex of pentagon and you got quadrangle and triangle. From them you got: 2x+6x+5x+3x+180-7x=360; 9x=180/:9 ; x=20.
I did it the same way😊
You are assuming that angle 7x is either acute or obtuse. We are told that the diagram may not be 100% true to the scale. We are not told that an angle being obtuse in the diagram means that it will be obtuse in the solution. Your solution is correct if 7x is obtuse. However, what if 7x is greater than 180° but less than 360°? When you connect the bottom apexes, the vertex of 7x will be below that line. If you don't make math errors, you will find the correct value of x.
✨Magic!✨
RUSSIA! Сумма углов в треугольнике 180 градусов, в четырёхугольнике 360 градусов, в пятиугольнике 540 градусов, и т. д. Преобразуем пятиугольник в четырёхугольник, для этогосоединим прямой линией углы 2х и 3х,
к полученной сумме углов добавим разницу 180-7х и приравняем это к 360 градусам:
2х+6х+5х+3х+180-7х=360; 9х=180, откуда х=180/9=20 градусов.
Thank you
The internal angles of a polygon sum to (n-2)180°, where n is the number of sides of the polygon. As this is a pentagon, the internal angles sum to (5-2)180° = 540°.
2x + 6x + 5x + 3x + (360°-7x) = 540°
16x + 360° - 7x = 540°
9x = 540° - 360° = 180°
x = 180°/9 = 20°
3*180=(2+6+5+3)x+(360-7x)---> x=20º.
Gracias y saludos.
Nice! φ = 30° → 9x = 6φ → x = 2φ/3
We may join vertices of angle 2x degrees
and 3x degrees
Then a quadrilateral will be formed.
Then for this quadrilateral the sum of angles is
6x +2x +3x +5x + 180 -7x = 360
> 9x =360 -180=180
> x =20
Hence x = 20 degrees
@ 1:33 All of my polygons have an infinite number of sides and I cannot tell the difference between any of em! This five sider made life a little easier for me today. 😊
Angles inside a pentagon total 540deg (due to((5-2)*180).
Angles in the shown pentagon are 16x + (360 - 7x), so 9x + 360 = 540
9x = 180
x = 20deg.
The answer is x = 20 degrees and I shall use that to refresh my understanding of geometry!!!
My way of solution is ▶
The interior sum of the angles of a Polygon (Pentagon):
n= 5
s(A)= (5-2)*180
s(A)= 540°
s(A)= 6x+5x+3x+2x+(360°- 7x)
540°= 16x-7x+360°
180°= 9x
x= 20°
The sum of angles within a polygon is (# sides - 2)*180. So, for a five sided polygon that sum is: 540 (180*3), which should be equal to: 2x + 6x + 5x + 3x +(360-7x). Solving for x = 20.
Let's find x:
.
..
...
....
.....
The interior angle sum for a polygon with n corners is given by:
(n − 2)*180°
Here we have five corners and five interior angles:
6x + 5x + 3x + (360° − 7x) + 2x = (5 − 2)*180°
9x + 360° = 540°
9x = 180°
⇒ x = 20°
Best regards from Germany
540= 360-7x+2x+3x+5x+6x
540= 360+9x
180= 9x
20= x
After seeing the 360-7x, the problem became a piece of cake
I couldn't remember that angle formula for polygons, but I know 4 angles is 360, so I drew a line from the back of the 7x angle to the perpendicular of the top line (between 5x and 6x), giving 2 4-sided shapes, assigning A and B to the resultant interior angles, where (A+B=360-7x):
A+90+6x+2x=360
B+90+5x+3×=360
Add both lines:
(A+B)+180+16×=720
Substitute:
(360-7x)+180+16x=720
-540 both sides
9x=180
×=20
(N-2)180°, where N is the number of sides
Easy.
2x+6x+5x+3x+(360-7x)=3*180=540...9x=180..x=20
x=20°
2x + 6x + 5x + 3x + (180° - 7x) = 360°
9x = 180°
x = 20°
2x+3x+5x+6x+360°-7x=540
So x=20°.❤❤❤
Solution:
Interior Angle Sum (S)
S = (n - 2) . 180°
S = (5 - 2) . 180°
S = (3) . 180°
S = 540°
2x + 360° - 7x + 3x + 5x + 6x = 540°
9x + 360° = 540°
9x = 540° - 360°
9x = 180°
x = 180°/9
x = 20° ✅
16X+ 180+(180-7x)=540=>x=20
Solution:
This pentagon can be divided into 3 triangles, so the sum of the angles in this pentagon is 3*180° = 540°. This means:
2x+360°-7x+3x+5x+6x = 540° |-360° ⟹
9x = 180° |/9 ⟹
x = 20°
STEP-BY-STEP RESOLUTION PROPOSAL :
01) Sum of Interior Angles of a Polygon : AP = (N - 2) * 180º; where N = Number of Sides.
02) Sum of a Pentagon Interior Angles = (5 - 2) * 180º = 3 * 180º = 540º
03) 2X + 3X + 5X + 6X + (360º - 7X) = 540º
04) 16X - 7X = 540º - 360º
05) 9X = 180º
06) X = 20º
ANSWER :
X equal 20º.
Great job!👍
Thanks for sharing ❤️🙏
360÷18=20)(×=20
UUHHH