Angles (Corresponding and Alternate) - Middle Grades

In the figure below what are the measurements for angles X , Y and Z. Note that line AB is parallel to Line CD.

Answer:
Angle X = 70 degrees
Angle Y = 60 degrees
Angle Z = 60 degrees

Explanation:
In order to find out what angle Z is we must know that angles on a straight line must all equal to 180 degrees. Therefore we will add the totals for the other two angles and subtract that from 180 to find our angle as follows:
180 – (70 + 50) =
180 – (120) = 60

To complete the rest of the problem we must know these two facts:

1. The total of the three angles in a triangle must equal 180 degrees.
2. When a line is parallel to a side of a triangle then the two corresponding angles must be
equal and the two alternate angles must be equal.

Therefore the angles X, Y and 50 in the triangle must equal 180 degree.

Line CD is parallel to line AB and part of line AB forms one side of the triangle that has the other three angles. which formsin the triangle then angles 70 and X are corresponding angles so they both equal each other and equal 70 degrees.

Also angles Y and Z are equal because they are alternate angles. Since we found out that angle Z equals 60 degree that means that angle Y must also equal 60 degrees.

For additional information on corresponding angles go to: Corresponding Angles.
For additional information on alternate angles go to: Alternate Interior Angles.

©Copyright 2007.Najwa S. Hirn. All rights reserved.