Before we start we need to remember that co-interior angles are supplementary, that is, they add up to 180°.
First diagram.
The angles shown are co-interior angles, then we have:
[tex]\begin{gathered} x+96+x+96=180 \\ 2x+192=180 \\ 2x=180-192 \\ 2x=-12 \\ x=-\frac{12}{2} \\ x=-6 \end{gathered}[/tex]
Once we have the value of x we plug it in the expression of the angle we want to know to find it:
[tex]-9+96=90[/tex]
Therefore, the angle is 90°.
Second diagram.
Once again the angles shown are co-interior then we have:
[tex]\begin{gathered} x+109+x+89=180 \\ 2x+198=180 \\ 2x=180-198 \\ 2x=-18 \\ x=-\frac{18}{2} \\ x=-9 \end{gathered}[/tex]
Plugging the value of x in the expression for the bolded diagram we have:
[tex]-9+89=80[/tex]
Therefore, the angle in the second diagram is 80°
