G.10 and *G.10 - Angles of Polygons

G.10    The student will solve real-world problems involving angles of polygons.

G.10  The student will solve problems, including practical problems, involving angles of convex polygons. This will include determining the

a)  sum of the interior and/or exterior angles;

b)  measure of an interior and/or exterior angle;

c)  number of sides of a regular polygon.

Bloom's Level:  Apply

BIG IDEAS

• I can create a home plate marker for softball field, exert enough force on a bolt to tighten it, and determine how many carpet squares to cover a gazebo floor.
• I will be able to figure out the sum of interior angles when I know the number of sides of a polygon, and with that knowledge find missing interior angle measurements.

UNDERSTANDING THE STANDARD

• A regular polygon will tessellate the plane if the measure of an interior angle is a factor of 360.
• Both regular and nonregular polygons can tessellate the plane.
• Two intersecting lines form angles with specific relationships.
• An exterior angle is formed by extending a side of a polygon.
• The exterior angle and the corresponding interior angle form a linear pair.
• The sum of the measures of the interior angles of a convex polygon may be found by dividing the interior of the polygon into nonoverlapping triangles.

·  In convex polygons, each interior angle has a measure less than 180°.

·  In concave polygons, one or more interior angles have a measure greater than 180°.

·  Two intersecting lines form angles with specific relationships.

·  An exterior angle is formed by extending a side of a polygon.

·  The exterior angle and the corresponding interior angle form a linear pair.

·  The sum of the measures of the interior angles of a convex polygon may be found by dividing the interior of the polygon into nonoverlapping triangles.

·  Both regular and nonregular polygons can tessellate the plane.

·  A regular polygon will tessellate the plane if the measure of an interior angle is a factor of 360.

·  The sum of the measures of the angles around a point in a tessellation is 360°.

·  Tessellations can be found in art, construction and nature.

ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

ANGLES OF POLYGONS

G.101  Solve real-world problems involving the measures of interior and exterior angles of polygons (all other polygons)

·  G.10abc1  Solve problems, including practical problems, involving angles of convex polygons.

G.103  Find the sum of the measures of the interior and exterior angles of a convex polygon.

·  G.10a1  Determine the sum of the measures of the interior and exterior angles of a convex polygon.

G.104  Find the measure of each interior exterior angles of the polygon.

·  G.10b1  Determine the measure of each interior and exterior angle of a regular polygon.

G.105  Find the number of sides of a regular polygon, given the measures of interior or exterior angles of the polygon.

·  G.10c1  Determine the number of sides of a regular polygon, given the measures of interior or exterior angles of the polygon.

TESSELLATIONS

G.102 Identify tessellations in art, construction, and nature.

· G.10b2 Determine angle measures of a regular polygon in a tessellation.

KEY VOCABULARY

angle, polygon, measure, interior angle, exterior angle, tessellation/tessellate, sum, convex polygon, regular, regular polygon, side, irregular/nonregular polygon, factor, plane, intersecting lines, corresponding interior angle, linear pair, uniform tessellation, semi-regular tessellation, regular tessellation, divide, nonoverlapping, triangle

Updated: Oct 27, 2017