Prerequisite Skills VOCABULARY CHECK

Copy and complete the statement.

1.1 and ? are vertical angles.

ANSWER 4

2.3 and ? are consecutive interior angles.

ANSWER 5

Prerequisite Skills VOCABULARY CHECK

Copy and complete the statement.

3.7 and ? are corresponding angles.

ANSWER 3

4.5 and ? are alternate interior angles.

ANSWER 4

Prerequisite Skills

Find the measure of the indicated angle.

6. If m3 = 105°, then m 2 = ? .

ANSWER 105°

7. If m1 = 98°, then m 3 = ? .

ANSWER 98°

SKILLS AND ALGEBRA CHECK

Prerequisite Skills SKILLS AND ALGEBRA CHECK

Find the measures of the three angles.

5. In ABC, m A = x°, m B = 3x°, and

m C = (4x – 12) ° .

ANSWER 24°, 72°, 84°

Diagonal: Connects two non-

consecutive vertices

Divides the shape into

triangles.

How many triangles in the pentagon?

8.1 Find Angle Measuresin Polygons

C

A

E

D

B

• How many triangles in a hexagon, quadrilateral?

• 4, 2

• What is the pattern?

• The number of triangles equals the # of sides minus 2

triangles = (n – 2)

• How many triangles in a 15-gon?

• 13

• So how many degrees in a pentagon?

• Number of triangles?

• 3

• Number of degree in each triangle?

• 180

• Total number of degrees in the pentagon?

• 540 = 3 * 180

• Degrees = (n – 2) * 180, where n = # of sides

Find the measure of the interior angles of the indicated convex polygon

• octagon• octagon = 8• (n-2) *180 = degrees• n=8• (8-2) * 180• 6 * 180• 1080 = degrees

Find the measure of the interior angles of the indicated convex polygon

• 13-gon• (n-2) * 180 = degrees• n=13• (13-2) * 180• 11* 180• 1980 = degrees

• How can we find the number of sides a shape has based on the sum of the interior angles?

• D = (n-2) * 180

• n = (D/180) + 2

• So how many sides is the figure with 1620 degrees?

• n = (1620/180) + 2

• n = 9 + 2

• n = 11

• The sum of the measures of the interior angles of a convex polygon is 1440. Classify the polygon by the number of sides.

• n = (Interior Angles/180) + 2

• n = (1440/180) + 2

• n = (8) +2

• n=10

Exterior Angles

• The sum of exterior

angles is always equal

to 360˚

Interior and Exterior

angles always add to

180

5

43

2

1

A

B

C D

E

Why Exterior Angles equal 360

• What are the measure of the interior angles?

180*4 = 720

720 / 6 = 120

• What are the exterior angles?

• 180 – 120 = 60• 60 * 6 = 360

• Regular Hexagon

Find the value of x in the diagram shown.

• x = 540 – (132+107+82+112)

• x = 107

82

112

132107

x

Find the value of n for each regular n-gon described

• Each interior angle of the regular n-gon has a measure of 156

• 156n = Interior Angles

• Interior Angles =(n-2)*180

• 156n = (n-2) * 180

• 156n = 180n – 360

• 156n – 180n = -360

• -24n = -360

• n = 15

Find the measure of an interior angle and an exterior angle for the indicated regular

polygon

• Regular 18-gon • Interior Angles• (n-2)*180 = 2880• 2880/18 = 160

• Exterior Angles• 180 – 160 = 20

EXAMPLE 3 Find an unknown interior angle measure

SOLUTION

The polygon is a quadrilateral. Use the Corollary to the Polygon Interior Angles Theorem to write an equation involving x. Then solve the equation.x° + 108° + 121° + 59° = 360°

Combine like terms.

Subtract 288 from each side.x = 72

ALGEBRA Find the value of x in the diagram shown.

x + 288 = 360

The value of x is 72.ANSWER

GUIDED PRACTICE for Example 3

Use the diagram at the right. Find m S and m T.

3.

103°, 103°ANSWER

The measures of three of the interior angles of a quadrilateral are 89°, 110°, and 46°. Find the measure of the fourth interior angle.

4.

115°ANSWER

EXAMPLE 4 Standardized Test Practice

SOLUTION

Use the Polygon Exterior Angles Theorem to write and solve an equation.

Polygon Exterior Angles Theoremx° + 2x° + 89° + 67° = 360°Combine like terms.3x + 156 = 360

Solve for x.x = 68

The correct answer is B.ANSWER

What is the value of x in the diagram shown?

a = 136°, b = 35°, c = 126°

136 + 35 + 126 + x = 360

297 + x = 360

x = 360 – 297

x = 63

GUIDED PRACTICE for Example 4

A convex hexagon has exterior angles with measures 34°, 49°, 58°, 67°, and 75°. What is the measure of an exterior angle at the sixth vertex?

5.

ANSWER 77°

Homework

• Pg. 510 – 511

3-15 odd 19, 25, 26, 32