Question

Find the measure of the remote exterior angle. m∠x=(198- 5n)°m∠y=(5n+37)°m∠z=(n+7)°A. 14 B. 21 C. 107 D. 128

Answer 1

Notice that the sum of the interior angles of a triangle is equal to 180°; therefore,

`y+z+a=180\degree`

Where a is the interior angle of the triangle that is not labeled in the diagram.

Furthermore, notice that angle
`x+a=180\degree`Then,

`\begin{gathered} \Rightarrow y+z+a=x+a \\ \Rightarrow y+z=x \\ \Rightarrow5n+37+n+7=198-5n \end{gathered}`

Solve for n as shown below

`\begin{gathered} \Rightarrow11n=198-44=154 \\ \Rightarrow n=14 \end{gathered}`

Finding angle x, given that n=14,

`\begin{gathered} n=14 \\ \Rightarrow x=198-5*14=198-70=128 \end{gathered}`

Thus, the measure of the remote exterior angle is