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Using Properties of Parallel Lines

Using Properties of Parallel Lines 1.11 - Solution

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Let's begin with recalling that vertical angles are a pair of opposite angles formed by intersecting lines. Now, we can draw two lines and a transversal and calculate the number of pairs of such angles.

Let's list all pairs of corresponding angles that we can find. 1 and 42 and 35 and 86 and 7\begin{gathered} {\color{#0000FF}{\angle 1}} \text{ and } {\color{#0000FF}{\angle 4}} \\ {\color{#FF0000}{\angle 2}} \text{ and } {\color{#FF0000}{\angle 3}} \\ \textcolor{purple}{\angle 5} \text{ and } \textcolor{purple}{\angle 8} \\ {\color{#009600}{\angle 6}} \text{ and } {\color{#009600}{\angle 7}} \end{gathered} Therefore, two lines and a transversal form 44 pairs of vertical angles.