Question

In the following figures, solve for x. Complete parts (a) through (c)

Answer 1

Step-by-step explanation:

Part A:

The image is given below as

Concept:

Using the linear pairs theorem, we will have that

`\begin{gathered} z+80^0=180^0 \\ substract\text{ 80 from both sides} \\ z+80-80=180-80 \\ z=100^0 \end{gathered}`

Also from the image of the question, we can deduce that

`y=55^0(vertical\text{ angles are equal\rparen}`

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

`180^0`

By substtituting the values, we will have

`\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}`

Hence,

The final answer for x in part A is

`x=25^0`

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

`\begin{gathered} 7x+2x=90^0 \\ 9x=90^0 \\ (9x)/(9)=(90)/(9) \\ x=10^0 \end{gathered}`

Hence,

The final answer for x in part B is

`x=10^0`