8-8 Angles in Polygons

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpSolve.

1. 72 + 18 + x = 180

2. 80 + 70 + x = 180

3. x + 42 + 90 = 180

4. 120 + x + 32 = 180

x = 90

x = 30

x = 48

Course 2

8-8 Angles in Polygons

x = 28

Problem of the Day

How many different rectangles are in the figure shown? 100

Course 2

8-8 Angles in Polygons

Learn to find the measures of angles in polygons.

Course 2

8-8 Angles in Polygons

Course 2

8-8 Angles in Polygons

If you tear off the corners of a triangle and put them together, you will find that they form a straight angle. This suggests that the sum of the measures of the angles in a triangle is 180°.

Course 2

8-8 Angles in Polygons

Angles of a Triangle

The sum of the measures of the angles in a triangle is 180°.

m1 + m2 + m3 = 180°

1 3

2

Find the measure of the unknown angle.

Additional Example 1: Finding an Angle Measure of in a Triangle

Course 2

8-8 Angles in Polygons

55°

80° x

80° + 55° + x = 180°

135° + x = 180°

–135° –135°

x = 45°

The measure of the unknown angle is 45°.

The sum of the measures of the angles is 180°.Combine like terms.

Subtract 135° from both sides.

Course 2

8-8 Angles in Polygons

Angles of a Quadrilateral

The sum of the measures of the angles in a quadrilateral is 360°.

m1 + m2 + m3 + m4 = 360°

1

2

4

3

Find the unknown angle measure in the quadrilateral.

Additional Example 2: Finding an Angle Measure of in a Quadrilateral

Course 2

8-8 Angles in Polygons

65° + 89° + 82° + x = 360°

236° + x = 360°

–236° –236°

x = 124°

The measure of the unknown angle is 124°.

The sum of the measures of the angles is 360°.

Combine like terms.

Subtract 236° from both sides.

65° x

89°

82°

Divide each polygon into triangles to find the sum of its angle measures.

Additional Example 3: Drawing Triangles to Find the Sum of Interior Angles

Course 2

8-8 Angles in Polygons

There are 6 triangles.

The sum of the angle measuresof an octagon is 1,080°.

6 · 180° = 1080°

Divide each polygon into triangles to find the sum of its angle measures.

Check It Out: Example 3

Course 2

8-8 Angles in Polygons

There are 4 triangles.

The sum of the angle measuresof a hexagon is 720°.

4 · 180° = 720°

Lesson Quiz

54°

37°

Insert Lesson Title Here

84°

720°

Course 2

8-8 Angles in Polygons

Find the measure of the unknown angle for each of the following.

1. a triangle with angle measures of 66° and 77°

2. a right triangle with one angle measure of 36°

3. an quadrilateral with angle measures of 144°, 84°, and 48°.

4. Divide a six-sided polygon into triangles to find the sum of its interior angles