Wingeom Exterior Angles

This construction is based on concepts and skills in your book.

Name Teacher Period

If you are not skilled in the use of a protractor go to this website for help:

Fill in this table, using figure 1. Record the measured angles both in the table and on the diagram.

Interior Angle / Measure with a
protractor / Exterior Angle / Calculate the angle using the fact that the interior and exterior angle, at a vertex, sum to 180º
<BAC / <HAB
<ABC / <IBC
<BCA / <JCA
Total = / Total =

Protractors are not precision instruments; therefore, your answer may deviate from the precise answer by a degree or so. For this figure, the precise answers are given in the geometric principle stated below.

Geometric Principle: Every triangle has interior angles that sum to 180º and exterior angles that sum to 360º.

Fill in this table, using figure 2. Record the measured angles both in the table and on the diagram.

Interior Angle / Measure with a protractor / Exterior Angle / Calculate angle using the fact that the interior and exterior angle, at a vertex, sum to 180º
<GDE / <KDG
<DEF / <LGF
<EFG / <MFE
<FGD / <NED
Total = / Total =

Draw a dashed segment connecting points D and F. You have divided the quadrilateral into two non-overlapping triangles, each of which has interior angles that sum to 180º.

Therefore you would expect the interior angles of a quadrilateral to sum to 2 x 180º.

Geometric Principle: Every quadrilateral (4 sides) has interior angles that sum to 360º and exterior angles that sum to 360º.

Fill in this table, using figure 3. Record the measured angles both in the table and on the diagram.

Interior angle / Measure with a
protractor / Exterior Angle / Calculate angle using the fact that the interior and exterior angle, at a vertex, sum to 180º
<BAE / <FAB
<CBA / <GBC
<DCB / <HCD
<EDC / <IDE
<AED / <JEA
Total = / Total =

Draw dashed segments connecting points A to C and A to D. You have divided the pentagon (5 sides) into three non-overlapping triangles, each of which has interior angles that sum to 180º. Therefore, you would expect the interior angles of a pentagon to sum to 3 x 180º.

Geometric Principle: Every pentagon (5 sides) has interior angles that sum to 540º and exterior angles that sum to 360º.

From our investigations, we can assert that the sum of the exterior angles of a polygon (many sides) always equals 360º. However, the sum of the interior angles depends upon the number of edges in the polygon.

Consider these polygons, based on the number of non-overlapping triangles, calculate the sum of the interior angles:

Sum of interior angles = / Sum of the interior angles =