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Home > CCG > Chapter 2 > Lesson 2.1.4 > Problem 2-41

2-41.

Find all missing angles in the diagrams below.  

What do you know about vertical angles? Alternate interior angles? What about adjacent angles that form a straight line?

  1. Two vertical parallel lines cut by two transversal lines. The given angle about the point of intersection of the top transversal and the right parallel line is the interior left angle, 75 degrees. The given angle about the point of intersection of the bottom transversal and the right parallel line is the interior left angle, 85 degrees.

  1. Two horizontal parallel lines cut by two transversal lines that intersect at 1 point with the top parallel line and at two points with the bottom parallel line. The given angle about the point of intersection of the top transversals and the top parallel line is the exterior middle angle, 30 degrees. The given angle about the point of intersection of the right transversal and the bottom parallel line is the exterior right angle, 110 degrees.

Fill in the missing values.

  1. Two vertical parallel lines cut by two transversal lines. The angles about the point of intersection of the top transversal & the right parallel line is the interior left angle, 75 degrees & the exterior right, 75 degrees. The angle about the point of intersection of the bottom transversal and the right parallel line is the interior left angle, 85 degrees.  The angle about the point of intersection of the bottom transversal and the left parallel line is the exterior right angle, 85 degrees.

  1. Two horizontal parallel lines cut by two transversal lines that intersect at 1 point with the top parallel line and at two points with the bottom parallel line. The given angle about the point of intersection of the top transversals and the top parallel line is the exterior middle angle, 30 degrees. The 30 plus the exterior right angle is, 110 degrees. The given angle about the point of intersection of the right transversal and the bottom parallel line is the exterior right angle, 110 degrees.