[tex](1)\\(3t-34^o)+(t+15^o)+(a+35^o)=180^o\\3t-34^o+t+15^o+a+35^o=180^o\\4t+a+16^o=180^o\ \ \ |subtract\ 16^o\ from\ both\ sides\\4t+a=164^o\ \ \ \ |subtract\ 4t\ from\ both\ sides\\a=164^o-4t\\\\(2)\\(a+35^o)+(t+47^o)=180^o\\a+35^o+t+47^o=180^o\\a+t+82^o=180^o\ \ \ |subtrct\ 82^o\ from\ both\ sides\\a+t=98^o\\\\subtitute\ (1)\ to\ (2):\\\\164^o-4t+t=98^o\\164^o-3t=98^o\ \ \ |subtract\ 164^o\ from\ both\ sides\\-3t=-66^o\ \ \ |divide\ both\ sides\ by\ (-3)\\\boxed{t=22}[/tex]
[tex]subtitute\ t=22^o\ to\ (1)\\\\a=164^o-4\cdot22^o\\a=164^o-88^o\\\boxed{a=76^o}\\\\Answer:\boxed{t=22^o\ and\ a=76^o}[/tex]
The equation (1) - In a triangle, the three interior angles always add to 180°.
The equation (2) - Angles on one side of a straight line will always add to 180°.
