Finding angle measures 1

The  exercise appears under the 8th Grade Math Mission. This exercise uses several facts about the angles to practice finding missing angles in geometric diagrams.

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


 * 1) Apply the triangle sum theorem: This problem provides a diagram with a triangle. The student is asked to use facts about the angles in triangles to find a missing angle.Fam1-1.png
 * 2) Apply the transversal angle theorems: This problem provides a diagram with a pair of parallel lines and a transversal. The student is asked to use facts about the angles in triangles to find a missing angle.Fam1-2.png
 * 3) Apply the basic angle theorems: This problem provides a diagram with a set of lines that intersect at a single point. The student is asked to use facts about the angles in triangles to find a missing angle.Fam1-3.png

Strategies
Knowledge and comfort with the angle theorems are instrumental to doing this exercise correctly.
 * 1) In triangles the sum of all angles in a triangle is 180 and the measure of an exterior angle is equal to the sum of the two remote interior angles.
 * 2) With transversals and parallel lines, alternate interior angles, corresponding angles, and alternate interior angles are congruent. Additionally, same-side interior and exterior angles are supplementary.
 * 3) With intersecting lines vertical angles are congruent, perpendicular lines form right angles, and the sum of the angles in a line is 180.

Real-life applications

 * 1) Geometric concepts, such as the ones used in this exercise, are instrumental in architecture (drafting), art and graphical design.
 * 2) Geometry is important for computer aided design.