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Andrew Little · Answer 1 · 2021-08-26T06:48:46+0000

Answer:

$m\angle D=64^(\circ)$

Explanation:

Given

$\triangle ABE\sim \triangle TCD$

Similar triangles have conruent corresponding angles, so

$m\angle A=m\angle T=61^(\circ)\\ \\m\angle B=m\angle C=55^(\circ)\\ \\m\angle E=m\angle D$

The sum of the measures of all interior angles of the triangle is always equal to 180°, so

$m\angle T+m\angle C+m\angle D=180^(\circ)\\ \\61^(\circ)+55^(\circ)+m\angle D=180^(\circ)\\ \\m\angle D=180^(\circ)-61^(\circ)-55^(\circ)=64^(\circ)$

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