a.
∠1 and ∠2 are supplementary angles, therefore:
[tex]\begin{gathered} m\angle1+m\angle2=180 \\ m\angle1=180-m\angle2 \\ m\angle1=180-98 \\ m\angle1=82 \end{gathered}[/tex]------------------------------------------------
b.
∠5 and (∠3 + ∠4) are supplementary, so:
[tex]\begin{gathered} m\angle5+m\angle3+m\angle4=180 \\ m\angle5=180-m\angle3-m\angle4 \\ m\angle5=180-23-59 \\ m\angle5=98 \end{gathered}[/tex]---------------------------------------------------
c. ∠4 can be found using the triangle sum theorem:
[tex]\begin{gathered} m\angle8+m\angle9+m\angle4=180 \\ m\angle4=180-m\angle9-m\angle8 \\ m\angle4=180-51-70 \\ m\angle4=59 \end{gathered}[/tex]-------------------------------------------
d. ∠6 and (∠7 + ∠8) are supplementary, so:
[tex]\begin{gathered} m\angle6+m\angle7+m\angle8=180 \\ m\angle6=180-m\angle7-m\angle8 \\ m\angle6=180-59-70 \\ m\angle6=51 \end{gathered}[/tex]-----------------------------------------------------------------
e.
∠7 can be found using the triangle sum theorem, so:
[tex]\begin{gathered} m\angle7+m\angle3+m\angle2=180 \\ m\angle7=180-m\angle3-m\angle2 \\ m\angle7=180-23-98 \\ m\angle7=59 \end{gathered}[/tex]-----------------------------------
f. ∠9 and ∠10 are supplementary, so:
[tex]\begin{gathered} m\angle9+m\angle10=180 \\ m\angle9=180-m\angle10 \\ m\angle9=180-129 \\ m\angle9=51 \end{gathered}[/tex]------------------------------------------------
g.
∠10 and (∠7 + ∠8) are corresponding angles, so:
[tex]\begin{gathered} m\angle10=m\angle7+m\angle8 \\ m\angle10=59+70 \\ m\angle10=129 \end{gathered}[/tex]