Question

Find the missing values of the variables. The diagram is not to scale. (Image attached below)thank you ! :)

Answer 1

`\begin{gathered} x=\text{ 99}\degree \\ y\text{ = 64}\degree \end{gathered}`

Step-by-step explanation:

Here, we want to get the value of x and y

From the given image, the angle y and 116 lie on a straight line

The sum of the angles on a straight line is 180 degrees

Thus:

`\begin{gathered} 116\text{ + y = 180} \\ y\text{ =180-116} \\ y\text{ = 64}\degree \end{gathered}`

The sum of the internal angles of a polygon can be calculated by the formula:

`180(n-2)`

where n is the number of sides the polygon has

In the case of the given question, n is 4

Substituting the value of n, we have it that:

`180(4-2)\text{ = 360 degrees}`

To get the value of x:

`\begin{gathered} x\text{ + y + 125 + 72 = 360} \\ But\text{ from above , y = 64}\degree \\ Substituting\text{ this:} \\ x\text{ + 64 + 125 + 72 = 360} \\ x\text{ = 360-125-64-72} \\ x\text{ = 99 } \end{gathered}`