In the diagram Below

Mathematics

1 answer:

xxMikexx [17]2 years ago

4 0

Answer:

∠UTC = 55°
∠UCD = 70°
∠BCT = 55°

Step-by-step explanation:

In this figure of overlapping parallelograms, each angle is related to the others by several different theorems involving triangles, parallelograms, and parallel lines. That is, there are several different ways one can arrive at the answers to this question.

∠UTC ≅ ∠UDC = 180° -∠EDU . . . opposite angles of parallelogram; linear pair

∠UTC = 180° -125° = 55°

∠UCD ≅ ∠TBC = 180° -∠TBA . . . . corresponding angles; linear pair

∠UCD = 180° -110° = 70°

∠BCT ≅ ∠UTC = 55° . . . . alternate interior angles

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