SWBAT: Identify the different Angle Relationships in Circles.

Angle Relationships in circles

Day 5

SWBAT: Identify the different Angle Relationships in Circles.

Warm Up: (page 40)

3y + 4y + 8y = 360

15y = 360

y = 24

𝟐∡ = 𝑩𝑪 𝟐𝒙 = 4(24) 𝟐𝒙 = 96

𝒙 = 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

Tangent- Tangent ∡

Two Chords (Central ∡)

Chord –Tangent ∡

𝟐 ∙ 𝒎∡𝒙 = 𝒇 − 𝒏

𝟐 ∙ 𝒎∡𝒙 = 𝒏

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

Secant- Secant ∡

Chord –

Chord ∡

Inscribed ∡

Tangent- Secant ∡

𝟐 ∙ 𝒎∡𝒙 = 𝒇 − 𝒏

𝟐 ∙ 𝒎∡𝒙 = 𝒇 − 𝒏

𝟐 ∙ 𝒎∡𝒙 = 𝒇 + 𝒏

𝟐 ∙ 𝒎∡𝒙 = 𝒏

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

ON

𝟐∡ = 𝒂𝒓𝒄

𝟐(𝟏𝟏𝟔˚) = 𝒏

𝟐𝟑𝟐˚ = 𝒏

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

INSIDE

𝟐 ∙ ∡ = 𝒇 + 𝒏

y˚ 𝟐 ∙ 𝒎∡𝒚 = 𝟐𝟖 + 𝟐𝟎

𝟐 ∙ 𝒎∡𝒚 = 𝟒𝟖

𝒎∡𝒚 = 𝟐𝟒˚

m∡𝒙 =180-24 = 156˚

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

OUTSIDE

𝟐 ∙ ∡ = 𝒇 − 𝒏 250°

𝟐 ∙ 𝒎∡𝒌 = 𝟐𝟓𝟎 − 𝟏𝟏𝟎

𝟐 ∙ 𝒎∡𝒌 = 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

𝟐 ∙ ∡ = 𝒇 − 𝒏

𝟐 ∙ 𝒙 = 𝟕𝟓 − 𝟐𝟗

𝟐𝒙 = 𝟒𝟔

𝒙 = 𝟐𝟑°

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

OUTSIDE

𝟐 ∙ ∡ = 𝒇 − 𝒏

𝟐 ∙ 𝒙 = 𝟏𝟒𝟎 − 𝟕𝟒

𝟐𝒙 = 𝟔𝟔

𝒙 = 𝟑𝟑°

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

𝟐𝒙 = 𝟕𝟎 𝒙 = 𝟑𝟓°

𝟐(𝟓𝟎°) = 𝒙

𝟏𝟎𝟎° = 𝒙

𝟐∡ = 𝒂𝒓𝒄 𝟐∡ = 𝒂𝒓𝒄

𝟐 ∙ ∡ = 𝒇 − 𝒏

𝟐 ∙ 𝒙 = 𝟗𝟎 − 𝟕𝟎 𝟐𝒙 = 𝟐𝟎

𝒙 = 𝟏𝟎° 𝟐 ∙ ∡ = 𝒇 − 𝒏

𝟐 ∙ 𝟒𝟎 = 𝒙 − 𝟐𝟓

𝟖𝟎 = 𝒙 − 𝟐𝟓

𝟏𝟎𝟓° = 𝒙

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

𝟖𝟎° + 𝒙° = 𝟏𝟖𝟎

𝒙° = 𝟏𝟎𝟎°

𝟐 ∙ 𝒙 = (𝟏𝟎𝟎 + 𝟖𝟎)

𝒙 = 𝟗𝟎°

𝟐𝒙 = 𝟏𝟖𝟎

𝟐 ∙ 𝟏𝟎𝟓 = (𝟏𝟎𝟎 + 𝒙)

𝟐𝟏𝟎 = 𝟏𝟎𝟎 + 𝒙

𝟏𝟏𝟎 = 𝒙

𝟐 ∙ ∡ = 𝒇 − 𝒏

𝟐 ∙ 𝒙 = 𝟏𝟏𝟎 − 𝟕𝟎

𝟐𝒙 = 𝟒𝟎

𝒙 = 𝟐𝟎°

𝟕𝟎

𝟐 ∙ ∡ = 𝒇 + 𝒏

𝟐 ∙ ∡ = 𝒇 + 𝒏

SWBAT: Identify the different Angle Relationships in Circles.

SWBAT: Identify the different Angle Relationships in Circles.

SWBAT: Identify the different Angle Relationships in Circles.

𝟐 ∙ 𝒙 = (𝟖𝟕 + 𝟑𝟓)

𝒎∡𝒙 = 𝟔𝟏°

𝟐𝒙 = 𝟏𝟐𝟐

𝟐 ∙ ∡ = 𝒇 + 𝒏

𝒙

SWBAT: Identify the different Angle Relationships in Circles.

𝟏𝟒𝟎 𝟒𝟎 𝒙

𝟐 ∙ ∡ = 𝒇 − 𝒏

𝟐 ∙ 𝟒𝟎 = 𝟏𝟒𝟎 − 𝒙

𝟖𝟎 = 𝟏𝟒𝟎 − 𝒙 𝒙 = 𝟔𝟎°

SWBAT: Identify the different Angle Relationships in Circles.

𝟏𝟏𝟎 𝒙 𝟐 ∙ ∡ = 𝒇 − 𝒏

𝟐 ∙ 𝒙 = 𝟐𝟓𝟎 − 𝟏𝟏𝟎

𝟐𝒙 = 𝟏𝟒𝟎

𝒙 = 𝟕𝟎°