Explanation:
Part A:
The image is given below as
Concept:
Using the linear pairs theorem, we will have that
[tex]\begin{gathered} z+80^0=180^0 \\ substract\text{ 80 from both sides} \\ z+80-80=180-80 \\ z=100^0 \end{gathered}[/tex]
Also from the image of the question, we can deduce that
[tex]y=55^0(vertical\text{ angles are equal\rparen}[/tex]
Hence,
To calculate the value of x, we will use the sum of angles in a triangle
The sum of angles in a triangle gives
[tex]180^0[/tex]
By substtituting the values, we will have
[tex]\begin{gathered} x+y+z=180^0 \\ y=55^0 \\ z=100^0 \\ x+y+z=180^{0} \\ x+55+100=180^0 \\ x+155=180^0 \\ x=180-155 \\ x=25^0 \end{gathered}[/tex]
Hence,
The final answer for x in part A is
[tex]x=25^0[/tex]
Part B:
From the image in the question we can see that angle segmen makes up a right angle
Hence,
We will have the relation below
[tex]\begin{gathered} 7x+2x=90^0 \\ 9x=90^0 \\ \frac{9x}{9}=\frac{90}{9} \\ x=10^0 \end{gathered}[/tex]
Hence,
The final answer for x in part B is
[tex]x=10^0[/tex]
