If \(L_1\) and \(L_2\) are parallel lines, then the angle \(\alpha\) measures:
-
\(300^{\circ}\)
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\(270^{\circ}\)
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\(210^{\circ}\)
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\(90^{\circ}\)
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\(110^{\circ}\)
Try to solve it before checking the answer.
\(270^{\circ}\)
Let’s draw the line \(L\) that is parallel to \(L_1\) and \(L_2\), and that passes through the vertex of the angle \(L_2\).
We have that:
\alpha = \beta + \theta \hspace{3em} \boldsymbol{(1)}
\]
Tenemos que:
\alpha = \beta + \theta \hspace{3em} \boldsymbol{(1)}
\]
\(\beta\) and the 60 degree angle are internal conjugate angles, hence these are supplementary angles. Then:
\beta + 60^{\circ} = 180^{\circ}
\Rightarrow \beta = 120^{\circ} \hspace{2em} \boldsymbol{(2)}
\]
\(\theta\) and the 150 degrees angle are alternate interior angles, hence these are congruent. Then:
\theta = 150^{\circ} \hspace{4em} \boldsymbol{(3)}
\]
Now, replacing (2) and (3) in (1):
\alpha = 120^{\circ} + 150^{\circ} = \boldsymbol{270^{\circ}}
\]