Please solve the 17th problem. Please do not provide any link. Q.17. In the following figure; AB is the largest and BC is the smallest side of triangle. Write the angles x$°$, y$°$ and z$°$ in ascending order of their values.

Dear Student,

Here , Exterior$\angle$ BAC + $\angle$ BAC = 180$°$                         ( Linear pair angles )
So,

x  + $\angle$ BAC = 180$°$   , By substituting value from given diagram

$\angle$ BAC  = 180$°$ - x

Similarly we get : $\angle$ ABC  = 180$°$ - y   and $\angle$ ACB  = 180$°$ - z

Then ,

$\angle$ BAC  = 180$°$ - x  , $\angle$ ABC  = 180$°$ - y   and $\angle$ ACB  = 180$°$ - z                      --- ( 1 )

i ) Given : AB is largest and BC is smallest side of given triangle  , So

AB > AC > BC

And we know theorem : In two unequal sides of triangle , the angle opposite to longer side is larger vice versa .

So ,

$\angle$ ACB > $\angle$ ABC >  $\angle$ BAC , Substitute values from equation 1 we get :

180$°$ - z > 180$°$ - y  > 180$°$ - x  , Now we subtract 180$°$ and get :

- z > - y > - x  , Now we multiply by ' - 1 ' and get :

z  <  y < x                                                                       ( Ans )