GEOMETRYWhat lies behind us and what lies before us are tiny matters compared to what lies within us.

Ralph Waldo Emerson

Today:– 11.1 Instruction– Practice

11.1 Angle Measures in Polygons

Objectives:• Find measure interior angles of

polygons• Find measure exterior angles

of polygons

Vocabulary: interior angles, exterior angles

polygon# of sides

# of triangles

Sum of interior angles

triangle

quadrilateral

pentagon

hexagon

heptagon

octagon

decagon

20-gon

n-gon

polygon# of sides

# of triangles

Sum of interior angles

triangle 3 1 1x180=180

quadrilateral

pentagon

hexagon

heptagon

octagon

decagon

20-gon

n-gon

polygon# of sides

# of triangles

Sum of interior angles

triangle 3 1 1x180=180

quadrilateral 4 2 2x180=360

pentagon

hexagon

heptagon

octagon

decagon

20-gon

n-gon

polygon# of sides

# of triangles

Sum of interior angles

triangle 3 1 1x180=180

quadrilateral 4 2 2x180=360

pentagon 5 3 3x180=540

hexagon 6 4 4x180=720

heptagon 7 5 5x180=900

octagon 8 6 6x180=1080

decagon 10 8 8x180=1440

20-gon 20 18 18x180=3240

n-gon

polygon# of sides

# of triangles

Sum of interior angles

triangle 3 1 1x180=180

quadrilateral 4 2 2x180=360

pentagon 5 3 3x180=540

hexagon 6 4 4x180=720

heptagon 7 5 5x180=900

octagon 8 6 6x180=1080

decagon 10 8 8x180=1440

20-gon 20 18 18x180=3240

n-gon n n - 2 (n-2)x180

Find the sum of the interior angles of a regular nonagon.

1260°

What is the measure of each interior angle?

140°

Find the measure of each interior angle of a regular quadrilateral.90°

Find the measure of each exterior angle of a equilateral triangle.

120°

Find exterior angle of the same regular quadrilateral. 90°

The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex is ___________.360

What is the measure of an exterior angle for regular hexagon?60°

A regular polygon has exterior angles of 18°, how many sides in this polygon.

20

A regular polygon has interior angles of 150°, how many sides in this polygon.

12

x

x

x

3x 2x

x = 67.5º

x + 20

x

x2x

2x

x = 85º

Find y.

60°

y

y2y

2y

11.1 Angle Measures in Polygons

What lies behind us and what lies before us are tiny matters compared to what lies within us.

Ralph Waldo Emerson

Assignment:• p 708 #1-7 odd

and p 712 #1, 2, 12 – 16