SWBAT: Identify the different Angle Relationships in Circles.

Angle Relationships in circles

Day 5

SWBAT: Identify the different Angle Relationships in Circles.

Warm Up (#’s 1 and 2): (page 40)

3n + 4n + 8n = 360

15n = 360

n = 24

4n = 4(24) = 96

4n

𝟐 · ∡ = 𝑨𝑹𝑪

𝟐 · ∡ = 𝟗𝟔

∡ = 48˚

SWBAT: Identify the different Angle Relationships in Circles.

Warm Up: (page 40)

132 + 82 = 214 𝟐 · ∡ = 𝑨𝑹𝑪

𝟐 · ∡ = 𝟐𝟏𝟒

∡ = 107˚

SWBAT: Identify the different Angle Relationships in Circles. (page 41)

Outside the Circle

On the Circle

Inside the Circle

Two Tangents

Two Radii (Central ∡)

Chord and Tangent

𝒎∡𝒙 = 𝟏

𝟐(𝒇 − 𝒏)

𝟐(𝒎∡𝒙) = 𝒏

𝒎∡𝒙 = 𝟏

𝟐𝒏

or

𝒎∡𝒙 = 𝒏

SWBAT: Identify the different Angle Relationships in Circles. (page 41)

Outside the Circle

Outside the Circle

On the Circle

Inside the Circle

Two Secants

Two Intersecting

Chords

Two Chords (Inscribed ∡)

Tangent and Secant

𝒎∡𝒙 = 𝟏

𝟐(𝒇 − 𝒏)

𝒎∡𝒙 = 𝟏

𝟐(𝒇 − 𝒏)

𝒎∡𝒙 = 𝟏

𝟐(𝒇 + 𝒏)

𝟐(𝒎∡𝒙) = 𝒏

SWBAT: Identify the different Angle Relationships in Circles. Example 1: (page 42)

ON

𝟐(𝒎∡𝒙) = 𝒏

𝟐(𝟏𝟏𝟔˚) = 𝒏

𝟐𝟑𝟐˚ = 𝒏

SWBAT: Identify the different Angle Relationships in Circles. Example 2: (page 42)

INSIDE

𝒎∡𝒚 = 𝟏

𝟐(𝒇 + 𝒏)

y˚ 𝒎∡𝒚 = 𝟏

𝟐(𝟐𝟖 + 𝟐𝟎)

𝒎∡𝒚 = 𝟏

𝟐(𝟒𝟖)

𝒎∡𝒚 = 𝟐𝟒˚ m∡𝒙=180-24

= 156 ̊

𝒎∡𝒙 = 𝟏

𝟐(𝒇 + 𝒏)

𝒎∡𝒙 = 𝟏

𝟐(𝟑𝟏𝟐)

𝒎∡𝒙 = 𝟏𝟓𝟔˚

SWBAT: Identify the different Angle Relationships in Circles. Example 3: (page 42)

OUTSIDE

𝒎∡𝒌 = 𝟏

𝟐(𝒇 − 𝒏)

250° 𝒎∡𝒌 =

𝟏

𝟐(𝟐𝟓𝟎 − 𝟏𝟏𝟎)

𝒎∡𝒌 = 𝟏

𝟐(𝟏𝟒𝟎)

𝒎∡𝒌 = 𝟕𝟎

SWBAT: Identify the different Angle Relationships in Circles. Example 4: (page 43)

𝒎∡𝒌+𝒎𝑳𝑱 = 𝟏𝟖𝟎

𝟑𝟒° +𝒎𝑳𝑱 = 𝟏𝟖𝟎°

𝒎𝑳𝑱 = 𝟏𝟒𝟔°

SWBAT: Identify the different Angle Relationships in Circles. Example 5: (page 43)

OUTSIDE

𝒎∡𝑵 = 𝟏

𝟐(𝒇 − 𝒏)

𝒎∡𝑵 = 𝟏

𝟐(𝟕𝟓 − 𝟐𝟗)

𝒎∡𝑵 = 𝟏

𝟐(𝟒𝟔)

𝒎∡𝑵 = 𝟐𝟑°

SWBAT: Identify the different Angle Relationships in Circles. Example 6: (page 43)

OUTSIDE

𝒎∡𝑹 = 𝟏

𝟐(𝒇 − 𝒏)

𝒎∡𝑹 = 𝟏

𝟐(𝟏𝟒𝟎 − 𝟕𝟒)

𝒎∡𝑹 = 𝟏

𝟐(𝟔𝟔)

𝒎∡𝑹 = 𝟑𝟑

SWBAT: Identify the different Angle Relationships in Circles. Key Questions: (page 44)

𝟐(𝒎∡𝒙) = 𝟕𝟎

𝒎∡𝒙 = 𝟑𝟓

𝟐(𝟓𝟎°) = 𝒙

𝟏𝟎𝟎° = 𝒙

𝒎∡𝒙 = 𝟏

𝟐(𝟗𝟎 − 𝟕𝟎)

𝒎∡𝒙 = 𝟏

𝟐(𝟐𝟎)

𝒎∡𝒙 = 𝟏𝟎 𝟒𝟎° = 𝟏

𝟐(𝒙 − 𝟐𝟓)

𝟖𝟎° = 𝒙 − 𝟐𝟓

𝟏𝟎𝟓° = 𝒙

SWBAT: Identify the different Angle Relationships in Circles. Key Questions: (page 44)

𝟖𝟎° + 𝒙° = 𝟏𝟖𝟎

𝒙° = 𝟏𝟎𝟎°

𝒎∡𝒙 = 𝟏

𝟐(𝟏𝟎𝟎 + 𝟖𝟎)

𝒎∡𝒙 = 𝟗𝟎°

𝒎∡𝒙 = 𝟏

𝟐(𝟏𝟖𝟎)

𝒎∡𝒙 = 𝟏

𝟐(𝟏𝟏𝟎 − 𝟕𝟎)

𝒎∡𝒙 = 𝟏

𝟐(𝟒𝟎)

𝒎∡𝒙 = 𝟐𝟎°

𝟏𝟎𝟓 = 𝟏

𝟐(𝟏𝟎𝟎 + 𝒙)

𝟐𝟏𝟎 = 𝟏𝟎𝟎 + 𝒙

𝟏𝟏𝟎 = 𝒙

SWBAT: Identify the different Angle Relationships in Circles. Challenge: (page 45)

SWBAT: Identify the different Angle Relationships in Circles. Summary: (page 45)

SWBAT: Identify the different Angle Relationships in Circles. Exit Ticket: (page 46)

SWBAT: Identify the different Angle Relationships in Circles. Exit Ticket: (page 46)