Equation practice with congruent angles

The  exercise appears under the 8th Grade Math Mission. This exercise uses congruent and supplementary angles with parallel lines to practice setting up and solving linear equations.

Types of Problems
There are two types of problems in this exercise:


 * 1) Use the congruent angles to find the variable: This problem provides a picture with two parallel lines and a transversal. Two congruent angles are described with variables and the student is expected to find the value of the variable.Epwca1.png
 * 2) Use the supplementary angles to find the variable: This problem provides a picture with two parallel lines and a transversal. Two supplementary angles are described with variables and the student is expected to find the value of the variable.Epwca2.png

Strategies
Knowledge of some of the angles theorems and postulates are helpful and an ability to solve linear equations is necessary for success on this exercise.
 * 1) The angles that are congruent to a given angle are called corresponding, alternate interior, alternate exterior and vertical.
 * 2) The angles that are supplementary to a given angle are those that form a linear pair, same-side interior, or same-side exterior.
 * 3) The picture should make some angles look obtuse and some angles look acute. As long as there are parallel lines, the angles that look congruent are and angles that don't look congruent are supplementary.

Real-life applications

 * 1) Many geometric concepts come up in the fields of architecture and graphical design.