Find the measure of an inscribed angle.

1. 6.14.3 Inscribed Angles
The student is able to (I can):
• Find the measure of an inscribed angle

2. inscribed angle An angle whose vertex is on the circle and
whose sides contain chords of the circle.
The measure of an inscribed angle is ½ the
measure of its intercepted arc.
•
H
A
I
R
∠ =
1
m AHR AR
2
= ⋅ ∠AR 2 m AHR

3. Example Find each measure:
1. m∠MAP
2.
M
A
P
110º
J
Y
O
24º24º24º24º
mJY

4. Example Find each measure:
1. m∠MAP
2.
= 2(24)
= 48º
M
A
P
110º
J
Y
O
24º24º24º24º
mJY
( )∠ =
1
m MAP mMP
2
= = °
1
(110) 55
2
= ∠mJY 2(m JOY)

5. If inscribed angles intercept the same arc,
then the angles are congruent.
R
E
A D
∠RED ≅ ∠RAD

6. An inscribed angle intercepts a semicircle if
and only if it is a right angle.
•

7. If a quadrilateral is inscribed in a circle, its
opposite angles are supplementary.
F
R
E
D
FRED is inscribed
in the circle.
m∠F + m∠E = 180º
m∠R + m∠D = 180º