# G.10 - 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.

### 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

2016 VDOE Curriculum Framework - G.10 Understanding

·  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

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

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

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

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

·  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: Aug 23, 2018