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NAME ______________________________________________ DATE
1-4
____________ PERIOD _____
Lesson Reading Guide
Angle Measure
Get Ready for the Lesson
Read the introduction to Lesson 1-4 in your textbook.
• A semicircle is half a circle. How many degrees are there in a semicircle?
• How many degrees are there in a quarter circle?
Read the Lesson
Remember What You Learned
3. A good way to remember related geometric ideas is to compare them and see how they
are alike and how they are different. Give some similarities and differences between
congruent segments and congruent angles.
Chapter 1
28
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. Match each description in the first column with one of the terms in the second column.
Some terms in the second column may be used more than once or not at all.
a. a figure made up of two noncollinear rays with a
1. vertex
common endpoint
2. angle bisector
b. angles whose degree measures are less than 90
3. opposite rays
c. angles that have the same measure
4. angle
d. angles whose degree measures are between 90 and 180
5. obtuse angles
e. a tool used to measure angles
6. congruent angles
f. the common endpoint of the rays that form an angle
7. right angles
g. a ray that divides an angle into two congruent angles
8. acute angles
9. compass
10. protractor
2. Use the figure to name each of the following.
E
a. a right angle
F
D
b. an obtuse angle
28⬚
28⬚ C
c. an acute angle
d. a point in the interior of ⬔EBC
A
B
G
e. a point in the exterior of ⬔EBA
f. the angle bisector of ⬔EBC
g. a point on ⬔CBE
h. the sides of ⬔ABF
i. a pair of opposite rays
j. the common vertex of all angles shown in the figure
k. a pair of congruent angles
l. the angle with the greatest measure
NAME ______________________________________________ DATE
1-4
____________ PERIOD _____
Study Guide and Intervention
Angle Measure
Measure Angles If two noncollinear rays have a common
endpoint, they form an angle. The rays are the sides of the angle.
The common endpoint is the vertex. The angle at the right can be
named as ⬔A, ⬔BAC, ⬔CAB, or ⬔1.
B
1
A
A right angle is an angle whose measure is 90. An acute angle
has measure less than 90. An obtuse angle has measure greater
than 90 but less than 180.
Example 1
S
R
1 2
C
Example 2
Measure each angle and
classify it as right, acute, or obtuse.
T
3
Q
P
E
D
a. Name all angles that have R as a
vertex.
Three angles are ⬔1, ⬔2, and ⬔3. For
other angles, use three letters to name
them: ⬔SRQ, ⬔PRT, and ⬔SRT.
A
B
a. ⬔ABD
Using a protractor, m⬔ABD ⫽ 50.
50 ⬍ 90, so ⬔ABD is an acute angle.
b. Name the sides of ⬔1.
៮៮៬, RP
៮៮៬
RS
b. ⬔DBC
Using a protractor, m⬔DBC ⫽ 115.
180 ⬎ 115 ⬎ 90, so ⬔DBC is an obtuse
angle.
c. ⬔EBC
Using a protractor, m⬔EBC ⫽ 90.
⬔EBC is a right angle.
Exercises
Refer to the figure.
A
B
4
1. Name the vertex of ⬔4.
1
D
2. Name the sides of ⬔BDC.
3
2
C
3. Write another name for ⬔DBC.
Measure each angle in the figure and classify it as right,
acute, or obtuse.
N
M
S
4. ⬔MPR
P
5. ⬔RPN
R
6. ⬔NPS
Chapter 1
29
Glencoe Geometry
Lesson 1-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
C
NAME ______________________________________________ DATE
1-4
Study Guide and Intervention
____________ PERIOD _____
(continued)
Angle Measure
Congruent Angles
Angles that have the same measure are
congruent angles. A ray that divides an angle into two congruent
angles is called an angle bisector. In the figure, ៮៮៬
PN is the angle
bisector of ⬔MPR. Point N lies in the interior of ⬔MPR and
⬔MPN ⬵ ⬔NPR.
M
N
P
R
Q
R
Example
Refer to the figure above. If m⬔MPN ⫽ 2x ⫹ 14 and
m⬔NPR ⫽ x ⫹ 34, find x and find m⬔MPR.
Since ៮៮៬
PN bisects ⬔MPR, ⬔MPN ⬵ ⬔NPR, or m⬔MPN ⫽ m⬔NPR.
2x ⫹ 14 ⫽ x ⫹ 34
2x ⫹ 14 ⫺ x ⫽ x ⫹ 34 ⫺ x
x ⫹ 14 ⫽ 34
x ⫹ 14 ⫺ 14 ⫽ 34 ⫺ 14
x ⫽ 20
m⬔NPR ⫽ (2x ⫹ 14) ⫹ (x ⫹ 34)
⫽ 54 ⫹ 54
⫽ 108
Exercises
៮៮៬ bisects ⬔PQT, and QP
៮៮៬ and QR
៮៮៬ are opposite rays.
QS
1. If m⬔PQT ⫽ 60 and m⬔PQS ⫽ 4x ⫹ 14, find the value of x.
S
T
2. If m⬔PQS ⫽ 3x ⫹ 13 and m⬔SQT ⫽ 6x ⫺ 2, find m⬔PQT.
៮៮៬ and BC
៮៮៬ are opposite rays, BF
៮៮៬ bisects ⬔CBE, and
BA
៮BD
៮៬ bisects ⬔ABE.
E
D
3. If m⬔EBF ⫽ 6x ⫹ 4 and m⬔CBF ⫽ 7x ⫺ 2, find m⬔EBC.
F
1
A
2 3
B
4
C
4. If m⬔1 ⫽ 4x ⫹ 10 and m⬔2 ⫽ 5x, find m⬔2.
5. If m⬔2 ⫽ 6y ⫹ 2 and m⬔1 ⫽ 8y ⫺ 14, find m⬔ABE.
6. Is ⬔DBF a right angle? Explain.
Chapter 1
30
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
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