Answer:
[tex]m\angle S = 35^\circ, \ m\angle T = 105^\circ,\ m\angle R = 105^\circ[/tex]
Step-by-step explanation:
Similar Triangles
Lines ST and QR are parallel. Thus, angles S and Q are congruent, and angles T and R are congruent.
Considering the triangle PQR, the sum of its internal angles must be 180°:
[tex]m\angle P + m\angle Q + m\angle R = 180^\circ[/tex]
Substituting the known values:
[tex]40^\circ + 35^\circ + m\angle R = 180^\circ[/tex]
Solving for R:
[tex]m\angle R = 180^\circ - 40^\circ - 35^\circ[/tex]
[tex]m\angle R = 105^\circ[/tex]
Angles S and Q are congruent, thus
[tex]m\angle S = 35^\circ[/tex]
Angles T and R are congruent, thus
[tex]m\angle T = 105^\circ[/tex]
Summarizing:
[tex]\mathbf{m\angle S = 35^\circ, \ m\angle T = 105^\circ,\ m\angle R = 105^\circ}[/tex]
