Answer:
[tex]m\angle D=64^{\circ}[/tex]
Step-by-step explanation:
Given
[tex]\triangle ABE\sim \triangle TCD[/tex]
Similar triangles have conruent corresponding angles, so
[tex]m\angle A=m\angle T=61^{\circ}\\ \\m\angle B=m\angle C=55^{\circ}\\ \\m\angle E=m\angle D[/tex]
The sum of the measures of all interior angles of the triangle is always equal to 180°, so
[tex]m\angle T+m\angle C+m\angle D=180^{\circ}\\ \\61^{\circ}+55^{\circ}+m\angle D=180^{\circ}\\ \\m\angle D=180^{\circ}-61^{\circ}-55^{\circ}=64^{\circ}[/tex]
