#### Math - 2017-18

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

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

G.10The student willsolveproblems, including practical problems, involving angles of convex polygons. This will includedeterminingthea) 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

*Adopted: 2009*

### 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.10_{1}
**Solve** real-world problems
involving the measures of interior and exterior angles of polygons (all other
polygons)

· G.10abc_{1} **Solve**
problems, including practical problems, involving angles of convex polygons.

G.10_{3}
**Find** the sum of the measures
of the interior and exterior angles of a convex polygon.

· G.10a_{1} **Determine**
the sum of the measures of the interior and exterior angles of a convex
polygon.

G.10_{4}
**Find** the measure of each
interior exterior angles of the polygon.

· G.10b_{1} **Determine**
the measure of each interior and exterior angle of a regular polygon.

G.10_{5}
**Find** the number of sides of a
regular polygon, given the measures of interior or exterior angles of the
polygon.

· G.10c_{1} **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*