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In the diagram Below

In the diagram Below-example-1
User Ctrlplusb
by
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1 Answer

1 vote

Answer:

  1. ∠UTC = 55°
  2. ∠UCD = 70°
  3. ∠BCT = 55°

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.

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UTC

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

∠UTC = 180° -125° = 55°

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UCD

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

∠UCD = 180° -110° = 70°

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BCT

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

User Quayshawn
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