Respuesta :
[tex]\boldsymbol{m\angle R, m\angle S, m\angle T}[/tex] are equal to [tex]\boldsymbol{60^{\circ},55^{\circ},65^{\circ}}[/tex] respectively.
According to angle sum property of a triangle, sum of all angles of a triangle is equal to [tex]\boldsymbol{180^{\circ}}[/tex]
Let [tex]m\angle R=x[/tex]
As [tex]m\angle T[/tex] is [tex]5^{\circ}[/tex] more than [tex]m\angle R[/tex],
[tex]m\angle T=5^{\circ}+m\angle R[/tex]
[tex]\boldsymbol{m\angle R=m\angle T-5^{\circ}}[/tex]
Also,
[tex]m\angle S[/tex] is [tex]10^{\circ}[/tex] less than [tex]m\angle T[/tex],
[tex]\boldsymbol{m\angle S=m\angle T-10^{\circ}}[/tex]
So,
[tex]\boldsymbol{m\angle R+m\angle S+m\angle T=180^{\circ}}[/tex]
[tex]m\angle T-5^{\circ}+m\angle T-10^{\circ}+m\angle T=180^{\circ}[/tex]
[tex]3m\angle T-5^{\circ}-10^{\circ}=180^{\circ}[/tex]
[tex]m\angle T=\frac{195^{\circ}}{3}[/tex]
[tex]\boldsymbol{=65^{\circ}}[/tex]
[tex]m\angle R=65^{\circ}-5^{\circ}[/tex]
[tex]\boldsymbol{=60^{\circ}}[/tex]
[tex]m\angle S=65^{\circ}-10^{\circ}[/tex]
[tex]\boldsymbol{=55^{\circ}}[/tex]
For more information:
https://brainly.com/question/16903368?referrer=searchResults
