Lines \(m_{1},m_{2},l_{1},l_{2}\), and are coplanar, and they are drawn such that \(l_{1}\) is parallel to \(l_{2}\), and \(m_{2}\) is perpendicular to \(l_{2}\). If the measure of angle 1 is 50 degrees, what is the measure in degrees of angle 2 in the figure below?
+9479 Here I labeled angle 3 .
Since l1 and l2 are parallel...
m∠2 = m∠1 + m∠3 Imagine "sliding over" l2 onto l1 to see why this is.
The problem says that m∠1 = 50° .
m∠2 = 50° + m∠3 l1 and l2 are parallel, and m2 is perpendicular to l2 .
So... m2 is perpendicular to l1 . This means m∠3 = 90º .
m∠2 = 50° + 90º
m∠2 = 140°
