Answer: [tex]\text{m}\angle T=45^{\circ}[/tex]
Step-by-step explanation:
Given: In ΔSTU, [tex]\text{m}\angle S = (2x+10)^{\circ}[/tex] , [tex]\text{m}\angle T = (3x-9)^{\circ}[/tex], [tex]\text{m}\angle U = (6x-19)^{\circ}[/tex]
To find: [tex]\text{m}\angle T[/tex].
We know that the sum of all the angles of a triangle is [tex]180^{\circ}[/tex].
In ΔSTU,
[tex]\text{m}\angle S+\text{m}\angle T+\text{m}\angle U=180^{\circ}\\\\ 2x+10+3x-9+6x-19=180\\\\ 11x-18=180\\\\11x =180+18\\\\11x=198\\\\x=\frac{198}{11}\\\\ x=18[/tex]
[tex]\text{m}\angle T = (3(18)-9)^{\circ}\\\\=(54-9)^{\circ}\\\\= 45^{\circ}[/tex]
Hence, [tex]\text{m}\angle T=45^{\circ}[/tex]
