Answer:
[tex]m\angle PSQ=45^o[/tex]
Step-by-step explanation:
we know that
[tex]m\angle PSR=m\angle PSQ+m\angle QSR[/tex] ---> by addition angle postulate
substitute the given values
[tex]99^o=(3x+18)^o+(9x-27)^o[/tex]
solve for x
[tex]99^o=(12x-9)^o[/tex]
[tex]12x=99+9[/tex]
[tex]12x=108[/tex]
[tex]x=9[/tex]
Find the measure of angle PSQ
[tex]m\angle PSQ=(3x+18)^o[/tex]
substitute the value of x
[tex]m\angle PSQ=(3(9)+18)=45^o[/tex]
