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Show that ABC is a straight line in each of the following diagrams, given angles around point B.

Mathematics

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Here are the solutions to the geometry problems:

b) Show that ABC is a straight line in each of the following diagrams:

  • Diagram (1):
  1. Identify the angles around point B on the line segment AC.

    The angles are $\angle DBA = 49^\circ$, $\angle DBE = 90^\circ$ (indicated by the square symbol), and $\angle EBC = 41^\circ$.
    
  2. Sum these angles.

    $$
    \angle DBA + \angle DBE + \angle EBC = 49^\circ + 90^\circ + 41^\circ = 180^\circ
    $$
    
  3. Conclude.

    Since
    
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