Question

The measure of angle 1 is greater than 97° and at most 115°. Graph the possible values of x. (9x + 7)

Answer 1

ANSWER and EXPLANATION

The measure of angle 1 is greater than 97° and at most 115° (that means less than or equal to)

This means that:

`\begin{gathered} <1\text{ > 97}\degree \\ <1\text{ }\leq\text{ 115}\degree \end{gathered}`

From the diagram, angle 1 is equal to (9x + 7). This is because they are alternate interior angles.

This therefore means that:

`\begin{gathered} 9x\text{ + 7 > 97}\degree \\ \text{and} \\ 9x\text{ + 7 }\leq\text{ 115}\degree \end{gathered}`

Solve for x:

`\begin{gathered} 9x\text{ > 97 - 7} \\ 9x\text{ > 90} \\ \text{Divide through by 9:} \\ x\text{ > 10} \\ \text{and} \\ 9x\text{ }\leq\text{ 115 - 7} \\ 9x\text{ }\leq\text{ 108} \\ \text{Divide through by 9:} \\ x\text{ }\leq\text{ 12} \\ \Rightarrow\text{ 10 < x }\leq12 \end{gathered}`

Therefore, the number line graph of the possible range of values of x is:

That is the number line.