91Ó°ÊÓ

The given diagram is:

From the given diagram it can be noticed that $∠BOC=∠COE=90°$.

By using the angle addition postulate it can be obtained that:

$∠COD+∠DOE=∠COE$.

Now,

$∠COD+∠DOE=∠COE$

$58+∠DOE=90$

$∠DOE=90−58$

$∠DOE=32$

$\mathrm{Therefore},\mathrm{the}\mathrm{measure}\mathrm{of}\mathrm{the}\mathrm{angle}∠DOE\mathrm{is}32°.$

From the given diagram it can be noticed that the angles∠DOEand∠BOAare vertical angles.

Therefore, by using the vertical angle theorem it can be said that the angles∠DOEand∠BOAare the congruent angles.

Therefore, $∠BOA=∠DOE$.

Now,

$∠BOA=∠DOE=32°$

Therefore, the measure of the angle ∠BOA is 32°.

From the given diagram it can be noticed that the angles∠AOCand∠CODlies on the same straight-lineAD.

Therefore, the sum of the angles∠AOCand∠CODis 180°.

Therefore, $∠AOC+∠COD=180°$.

Now,

$∠AOC+∠COD=180$

$∠AOC+58=180$

$∠AOC=180−58$

$∠AOC=122$

Therefore, the measure of the angle∠AOCis122°.