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Name: ______________________________________________________________
Date: ______________________ Period: ______
Chapter 13: Circle Arcs & Angles
Topic 1: Angle Relationships – Central & Inscribed
1) Central Angle
The degree measure of an arc is ________________________________
___________________________________________________________
__________________________________________________________
̂ =___________.
If 𝑚 < 𝐴𝑃𝐵 = 60°, then 𝑚𝐴𝐵
According to the provided circle:
Major Arc = _______________
Minor Arc = ______________
A circle gets it’s name from the center. Therefore, the diagram above is called Circle P.
Examples:
1)
̂ = _______________
𝑚𝐴𝐵
4)
2)
3)
̂ = _______________
𝑚𝐴𝐵
𝑚 < 𝐴𝑃𝐵 = ______________
Given: Circle P, 𝑚 < 𝐵𝑃𝐶 = 15°
Find:
a) 𝑚 < 𝐴𝑃𝐶 = ____________________
̂ = ___________________
b) 𝑚 𝐴𝐶
̂ = ___________________
c) 𝑚 𝐵𝐶
̂ = ___________________
d) 𝑚 𝐴𝐵
̂ = ___________________
e) 𝑚 𝐴𝐵𝐶
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2) Inscribed Angle
To find the measure of an inscribed angle, we _____________________
__________________________________________________________.
Formula: ________________________________________
Examples:
̂ = 140°
1) Find 𝑚 < 𝐴 when 𝑚 𝐵𝐶
̂ = 60°
2) Find 𝑚 < 𝑁 when 𝑚 𝑀𝑂
̂ = ________________
3) Find 𝑚 𝐴𝐶
𝑚 < 𝐴 = ______________
𝑚 < 𝐶 = ______________
̂ = _______________
𝑚 𝐴𝐵
Mixed Examples (Common Core)
4) In the figure below, O is the center of the circle and segment AD is a diameter.
a.) Find m<AOB.
b.) If m<AOB:m<COD = 3:4, what is m<BOC?
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5) In the circle shown, BC is a diameter with center A. m<CBE = 26o and m<BDA = 18o.
̂.
a.) Find the measure of 𝐶𝐸
b.) Find m<BAE.
c.) Find m<DAB.
6) The diagram below is of Circle A. Use the information given to find the measure of the labeled angles.
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Name: ______________________________________________________________
Date: ______________________ Period: ______
Topic 1: Angle Relationships – Central & Inscribed
Complete the following examples. Show all work, including formulas for free-response questions. A correct
answer with no work shown will not receive credit on a test or quiz.
1.) In the diagram below of circle O, m<ABC = 24. What is the m<AOC?
(1) 12
(2) 24
(3) 48
(4) 60
2.) As shown in the diagram below, quadrilateral DEFG is inscribed in a circle and m<D = 86.
̂.
a.) Determine and state 𝐺𝐹𝐸
b.) Determine and state m<F.
3.) Given Circle A, the m<B = 32o. Find m<ACD.
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̂ : 𝐶𝐸
̂ : 𝐸𝐷
̂ : 𝐷𝐵
̂ = 1: 2: 3: 4. Find the following measures.
4.) In circle A, 𝐵𝐶
̂
a.) 𝑚𝐸𝐷
b.) m<BAC
c.) m<DAE
̂
d.) 𝑚𝐶𝐸𝐷
̂ = 𝑚𝐵𝐹
̂ and <FED = 66o.
5.) Use the diagram below to find the measure of <BCD. Given: 𝑚𝐷𝐵
Review Questions:
6.) What are the coordinates of the midpoint of the line segment with endpoints (2,-5) and (8,3)?
(1) (3,-4)
(2) (3,-1)
(3) (5,-4)
(4) (5,-1)
7.) If two sides of a triangle have lengths of 4 and 10, the third side could be
(1) 8
(2) 2
(3) 16
(4) 4
8.) Write an equation of a line that is parallel to the line whose equation is 3y = x + 6 and passes through the
point (-3,4)
9.) Quadrilateral HYPE has vertices H(2,3), Y(1,7), P(-2,7), and E(-2,4). State and label the coordinates of the
vertices H”Y”P”E” after the composition transformations 𝑟𝑥−𝑎𝑥𝑖𝑠 ∘ 𝑇5,−3.
10.) The sum of the interior angles of a regular polygon is 540o. Determine and state the number of degrees
in one interior angle of the polygon.
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