Angles in a circle add up to 360 degrees.
- [tex]\mathbf{x = 21}[/tex]
- [tex]\mathbf{GK = 167}[/tex]
- [tex]\mathbf{HJ = 98}[/tex]
- [tex]\mathbf{HGJ = 262}[/tex]
- [tex]\mathbf{GKJ = 201}[/tex]
The given parameters are:
[tex]\mathbf{GH = 61}[/tex]
[tex]\mathbf{HJ = 5x - 7}[/tex]
[tex]\mathbf{JK = 34}[/tex]
[tex]\mathbf{KG = 9x - 22}[/tex]
The sum of angles in a circle is 360 degrees.
So, we have:
[tex]\mathbf{GH + HJ + JK + KG=360}[/tex]
So, we have:
[tex]\mathbf{(9x-22) + 61 + (5x-7) + 34 = 360}[/tex]
[tex]\mathbf{14x = 294}[/tex]
Divide both sides by 14
[tex]\mathbf{x = 21}[/tex]
GK is calculated as:
[tex]\mathbf{GK = 9x - 22}[/tex]
[tex]\mathbf{GK = 9 \times 21 - 22}[/tex]
[tex]\mathbf{GK = 167}[/tex]
HJ is calculated as:
[tex]\mathbf{HJ = 5x - 7}[/tex]
[tex]\mathbf{HJ = 5 \times 21 - 7}[/tex]
[tex]\mathbf{HJ = 98}[/tex]
HGJ is calculated as:
[tex]\mathbf{HGJ = HG + GK + KJ}[/tex]
[tex]\mathbf{HGJ = 61 + 167 + 34}[/tex]
[tex]\mathbf{HGJ = 262}[/tex]
GKJ is calculated as:
[tex]\mathbf{GKJ =GK + KJ}[/tex]
[tex]\mathbf{GKJ = 167 + 34}[/tex]
[tex]\mathbf{GKJ = 201}[/tex]
Read more about angles in a circle at:
https://brainly.com/question/12260532
