Find the angle between parallel lines

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There is a line perpendicular to $AB$ and $DE$ passing through $C$. Say this line meets $AB$ at $X$ and $DE$ at $Y$. Then using the two right-angled triangles, $\angle ACX=90-42=48^{\circ}$ and $\angle DCY=90-54=36^{\circ}$. Since angles on a straight line sum to $180^{\circ}$, $\angle ACD=180-48-36=96^{\circ}$.

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JFC
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JFC

Updated on August 19, 2020

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  • JFC
    JFC about 3 years

    I am trying to solve the following problem.
    Given: $$\overleftrightarrow{AB} \parallel \overleftrightarrow{DE}$$ And the measures of angles $$\angle BAC = 42 ^{\circ}$$ $$\angle EDC= 54 ^{\circ}$$ Find the measure of angle $$\angle ACD$$ How would you approach to solve the problem. I have tried as recommended on book to assume that there is one parallel line passing through point $C$, but i couldn't produce an answer. What is your advice?
    Attached follows the geometric representationFigure 1 Geometric Model

    • Paul
      Paul about 5 years
      Draw a line through $C$ which is parallel to the other lines. Then the angle you want is the sum of 2 angles whose measure are easy to find.
    • JFC
      JFC about 5 years
      @Paul I appreciate.
  • JFC
    JFC about 5 years
    On the same figure if we make $\overleftrightarrow{AC}$ Transversal and draw parallel line $l$ through point $C$, this seems that angle between Transversal $\overleftrightarrow{AC}$ and parallel line $l$ is congruent to $\angle BAC$
  • JFC
    JFC about 5 years
    i mean inner right angle between Transversal $\overleftrightarrow{AC}$ and parallel line $l$
  • A. Goodier
    A. Goodier about 5 years
    @JFC Yes, you're right, because alternate angles are equal
  • JFC
    JFC about 5 years
    Thanks for the answer.