Geometry is a mathematical discipline that focuses on the properties and relationships between points, lines, surfaces and solids. Geometric figures are made up of lines, called sides or edges and points called vertices. Geometric shapes are classified by their individual characteristics, one of those being the measure of angles within the shape. For example, triangles have three angles whose sum equals 180 degrees, while quadrilaterals have four angles whose sum equals 360 degrees. Being able to determine the value of angles helps students to classify lines and shapes.

Find the value of X in triangles by subtracting known angle measurements from 180 degrees. Since the value of all angles within a triangle must equal 180 degrees, if you know at least two angles, you can subtract them from 180 to find the missing third angle. If you are working with equilateral triangles, divide 180 by three to find the value of X. All of the angles of an equilateral triangle are equal.

Solve for X in interesting lines by finding the value of one adjacent angle and subtracting it from 180 degrees. Adjacent angles are angles that are side-by-side. The sum of adjacent angles equals 180 degrees. Opposite angles are equal, so if you know the value of one angle, its opposite partner will have the same value. For example, if the value of one angle is 75 degrees its adjacent angle will be 105 degrees and its opposite angle will also be 75 degrees. Similarly, the adjacent angles opposite partner will measure 105 degrees as well.

Determine the value of X in angles of parallel lines that are intersected by a third line by finding the value each angle at the intersection of one of the parallel lines. Use the principles for finding the value of adjacent and opposite angles to find one set of intersecting angles. The value of the angles of the second parallel line intersection will be the same as its parallel partner. For example, if the value of the intersecting angles in line one are 120 and 60 degrees, the value of the intersecting angles in line two will also be 120 and 60 degrees.

#### References

- Thinkzone.wlonk.com; Elementary Geometry; Keith Enevoldsen
- "Everyday Mathematics Student Reference Book: Grade 5"; The University of Chicago School Mathematics Project; 2007

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