Transcript Angles and Arcs

Angles and Arcs
Central Angles – An angle in a circle that has
the center as its vertex and two radii as its
sides.
Sum of Central Angles – The sum of the
measures of the central angles of a circle
with no interior points in common is 360
degrees.
Angles and Arcs
Arc – A collection of the points that make up a circle. The
measure of an arc is related to the measure of its central
angle.
Minor Arc – An arc that is less than half of the circle. Its
degree measure is equal to the measure of its central angle.
It is named using the endpoints of the arc.
Major Arc – An arc that is more than half of the circle. Its
degree measure is equal to 360 minus the measure of its
minor arc. It is named using the endpoints of the arc and a
point between them.
Semicircle – An arc that is half of the circle. Its degree
measure is equal to 180. It is named using the endpoints
and a point between them.
Angles and Arcs
Theorem 10.1
• In the same or congruent circles, two arcs are
congruent if and only if their corresponding
central angles are congruent.
Arc Addition Postulate
• The measure of an arc formed by two adjacent
arcs is the sum of the measures of the two arcs.
Arc Length
• The length of an arc is (m/360) times the
circumference of the circle, where m is the
measure of the corresponding central angle.
ALGEBRA Refer to
a. Find m
Answer: 65
b. Find m
Answer: 40
.
In
and
bisects
a.
Answer: 54
b.
Answer: 72
c.
Answer: 234
are diameters,
Find each measure.
and
SPEED LIMITS This graph shows the percent of U.S.
states that have each speed limit on their interstate
highways.
a. Find the measurement of the central angles
representing each category. List them from least to
greatest.
Answer:
b. Is the arc for the wedge for 65 mph congruent to the
combined arcs for the wedges for 55 mph and 70 mph?
Answer: no
In
and
. Find the length of
Answer:
units or about 49.48 units
.