Question

use your theorem from 2-37 about the angles in a triangle to find in the diagram below. show all work.

Answer 1

We have that, for any triangle, the sum of all its angles equals 180. In this case, we have the following:

`96+2x+(x+12)=180`

Now we solve for x to get the following:

`\begin{gathered} 96+2x+x+12=180 \\ \Rightarrow2x+x=180-96-12 \\ \Rightarrow3x=72 \\ \Rightarrow x=(72)/(3)=24 \\ x=24 \end{gathered}`

We have that x = 24, now to find the angles, we substitute this value on each expression:

`\begin{gathered} 2x \\ x=24 \\ \Rightarrow2(24)=48 \\ x+12 \\ \Rightarrow24+12=36 \end{gathered}`

therefore, the remaining angles are 48° and 36°