Angle Relationships - CYU - BHNmath

ANGLE RELATIONSHIPS

BIG IDEAS: ? The sum of a polygon's interior angles is equal to 180? multiplied by two

less than its number of sides ? The sum of a polygon's exterior angles is always 360? ? Many equal angles are created when a transversal intersects parallel lines

LEARNING GOALS AND SKILL DEVELOPMENT: You know you have met the goals for this lesson when you can:

EMERGING

LEARNING GOALS

Determine the sum of the interior angles of various polygons

Determine the value of an unknown angle in a polygon Determine the value of an angle in a complementary, supplementary or opposite angle pair Determine unknown angles involving parallel lines intersected by a transversal

ANCHOR QUESTIONS

2, 3

4

5

6, 13abc

LEARNING GOALS

Determine the number of sides a polygon has given the sum of its interior angles

Use angle relationships to determine unknown angles

ANCHOR QUESTIONS

10

13def, 14

SKILL BUILDING QUESTIONS

1

2

3

4

5

6

7 13abc

SKILL BUILDING QUESTIONS

8

9

10

11

12 13def 14

15

16

EVOLVING

LEARNING GOALS

Determine unknown angles by writing and simplifying equations to solve for the unknown angle

ANCHOR QUESTIONS

17

SKILL BUILDING QUESTIONS

17

18

19

20

EXTENDING

Angle Relationships

BUILD YOUR SKILLS

1. What is the sum of a triangle's interior angles?

2. For each of the following polygons, i) copy the figure on a separate page and draw line segments from one vertex to the other vertices. ii) state the number of triangles created as a result of part (i).

iii) use your answer from part (ii) to determine the sum of the polygon's interior angles.

a)

b)

3. State the sum of the interior angles for each polygon.

a)

b)

c)

d)

4. Determine the value of angle x in each polygon.

a)

b)

c)

5. Determine the value of angle x in each diagram.

a)

b)

c)

Angle Relationships

6. What is an exterior angle of a polygon? You may wish to support your explanation with a diagram.

7. Determine the values of angles a, b, c, d, e, f and g in the diagram on the right.

8. Determine the value of each interior angle in a regular polygon with the given number of sides. a) 3 sides b) 4 sides c) 5 sides d) 8 sides e) 10 sides f) 30 sides

9. A regular polygon has n sides. a) State a procedure that can be used to determine the value of each interior angle. b) Create a formula that can be used to determine the value of each interior angle.

10. The sum of a polygon's interior angles is 1980?. How many sides does the polygon have?

11. Determine the value of angle x in each diagram.

a)

b)

c)

12. James is told that the sum of a polygon's exterior angles is 360?. Based on this information, can he determine how many sides the polygon has? Explain.

Angle Relationships

13. Determine the value of angle x in each diagram.

a)

b)

c)

d)

e)

f)

14. Determine the values of angles x and y in each diagram.

a)

b)

c)

Angle Relationships

15. Determine the values of angles x and y in the Progress Pride Flag shown below.

x

y

45?

16. Tiles used for floors and walls often have the shape of regular polygons. a) In order for these tiles to fit together snugly, what must be true about their interior angles? Explain. b) Which regular polygons are suitable for tiling?

17. Determine the value of angle x in each diagram.

a)

b)

c)

d)

e)

f)

Angle Relationships

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