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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)