Page 170 - Math Course 3 (Book 2)

Inscribed Angles

Angles of an Inscribed Quadrilateral
Your Turn!

Example Inscribed Arcs and Probability

PROBABILITY
Quadrilateral QRST is inscribed in ⊙M. Points A and X are on a circle so that mAX = 84.
If m∠Q = 87 and m∠R = 102. Find m∠S and m∠T.
Suppose point B is randomly located on the same
Draw a sketch of this situation. circle so that it does not coincinde with A or X.
What is the probability that m∠ABX = 42?

Q A. 7 B. 1
R 30 2
87° 102° C. 4 D. 23
5
30
M
Answer

S
T
Angles of an Inscribed Triangle
ALGEBRA
To find m∠S, we need to know mRQT.
Triangles MNO and MPO are inscribed in ⊙D with
To find mRQT, first find mRST. MN ≅ OP. Find m∠1 if m∠2 = 4x – 8 and
m∠3 = 3x + 9.
mRST = 2(m∠Q) Inscribed Angle Theorem
M N
= 2(87) or 174 m∠Q = 87 2
4
mRST + mRQT = 360 Sum of arcs in circle = 360 D

174 + mRQT = 360 mRST = 174

mRQT = 186 Subtract 174 from each side. 1 3

mRQT = 2(m∠S) Inscribed Angle Theorem. P O
A. 45
186 = 2(m∠S) Substitution. B. 90
C. 180
93 = m∠S Divide each side by 2. D. 80

Since we now know three angles of a quadrilateral, Answer
we can easily find the fourth.

360° in a Triangles MNO and MPO are inscribed in ⊙D with
m∠Q + m∠R + m∠S + m∠T = 360
quadrilateral MN ≅ OP. Find m∠2 if m∠2 = 4x – 8 and
87 + 102 + 93 + m∠T = 360 Substitution m∠3 = 3x + 9.
A. 17
m∠T = 78 Subtraction B. 76
C. 60
D. 42
Answer m∠S = 93; m∠T = 78
Answer

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