Corresponding angles (b=g) and vertical angles (c=f) are equal. Opposite angles on the transversal (a+h) add up to 180°. Alternate angles (e≠g) differ.
a.Angles b and g are congruent. This is because they are corresponding angles. Corresponding angles are formed when two lines are cut by a transversal, and they are equal. In the diagram, the transversal is the new dock, and lines b and g are the two sides of a slip that it cuts across.
b.The measures of angles b and c have a sum of 180 degrees. This is because they are supplementary angles. Supplementary angles are two angles that add up to 180 degrees. In the diagram, lines a and h are on opposite sides of the transversal, so they are supplementary angles.
c.Angles c and f are vertical angles. Vertical angles are formed when two lines intersect, and they are equal. In the diagram, the two lines are the new dock and the edge of the existing dock, and lines c and f are the angles formed where they intersect.
d.The measures of angles a and h have a sum of 180 degrees. This is because they are supplementary angles. Supplementary angles are two angles that add up to 180 degrees. In the diagram, lines a and h are on opposite sides of the transversal, so they are supplementary angles.
e.Angles e and g are not congruent. This is because they are alternate angles. Alternate angles are formed when two lines are cut by a transversal, and they are not equal. In the diagram, lines e and g are on opposite sides of the transversal, so they are alternate angles.