Download 4-2 Practice A Angle Relationships in Triangles

Name
LESSON
4-2
Date
Class
Practice A
Angle Relationships in Triangles
Use the figure for Exercises 1–3. Name all the angles that fit the definition of
each vocabulary word.
1. exterior angle
2. remote interior angles to ⬔6
3. interior angle
⬔1, ⬔4, ⬔6
⬔2, ⬔3
⬔2, ⬔3, ⬔5
For Exercises 4–7, fill in the blanks to complete each theorem or corollary.
4. The measure of each angle of an
equiangular
triangle is 60°.
180⬚
5. The sum of the angle measures of a triangle is
6. The acute angles of a
right
exterior angle
.
triangle are complementary.
7. The measure of an
of the measures of its remote interior angles.
of a triangle is equal to the sum
Find the measure of each angle.
!
30°
#
35°
$
"
'
70⬚
9. m⬔F
(
,
130°
)
65°
*
60⬚
10. m⬔G
0
X°
%
&
115⬚
8. m⬔B
20°
65⬚
11. m⬔L
3
1
+
40°
35°
9
5
2
12. m⬔P
80°
4
6
35⬚
7
8
13. m⬔VWY
14. When a person’s joint is injured, the person often goes through
rehabilitation under the supervision of a doctor or physical
therapist to make sure the joint heals well. Rehabilitation
involves stretching and exercises. The figure shows a leg
bending at the knee during a rehabilitation session. Use
what you know about triangles to find the angle measure that
the knee is bent from the horizontal (fully extended) position.
120⬚
—
—
—
110⬚
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
11
Holt Geometry
Name
LESSON
4-2
Date
Class
Practice B
Angle Relationships in Triangles
1. An area in central North Carolina is known as
the Research Triangle because of the relatively
.
Durham
large number of high-tech companies and research
10.7 mi
universities located there. Duke University, the
21.4 mi
Chapel
University of North Carolina at Chapel Hill, and
Hill
25.7 mi
North Carolina State University are all within this
Raleigh
area. The Research Triangle is roughly bounded
by the cities of Chapel Hill, Durham, and Raleigh.
From Chapel Hill, the angle between Durham and Raleigh
measures 54.8⬚. From Raleigh, the angle between Chapel Hill
and Durham measures 24.1⬚. Find the angle between
101.1⬚
Chapel Hill and Raleigh from Durham.
2. The acute angles of right triangle ABC are congruent.
Find their measures.
45⬚
The measure of one of the acute angles in a right triangle is given. Find the
measure of the other acute angle.
45.1⬚
3. 44.9⬚
4. (90 ⫺ z)⬚
z⬚
89.7⬚
5. 0.3⬚
Find each angle measure.
0
$
# 120°
23°
(5X 1)°
(9X 2)°
!
2
3
"
60⬚
6. m⬔B
1
47⬚
7. m⬔PRS
8. In 䉭LMN, the measure of an exterior angle at N measures 99⬚.
1 x ⬚ and m⬔M ⫽ __
2 x⬚. Find m⬔L, m⬔M, and m⬔LNM.
m⬔L ⫽ __
3
3
9. m⬔E and m⬔G
44⬚; 44⬚
10. m⬔T and m⬔V
4
%
5
&
(5X 4)°
108⬚; 108⬚
(10N 2)°
(6X 4)°
$
33⬚; 66⬚; 81⬚
7
(
(9N 9)°
'
6
11. In 䉭ABC and 䉭DEF, m⬔A ⫽ m⬔D and m⬔B ⫽ m⬔E. Find m⬔F if an exterior
angle at A measures 107⬚, m⬔B ⫽ (5x ⫹ 2)⬚, and m⬔C ⫽ (5x ⫹ 5)⬚.
12. The angle measures of a triangle are in the ratio 3 : 4 : 3. Find the angle
measures of the triangle.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
12
55⬚
54⬚; 72⬚; 54⬚
Holt Geometry
Name
LESSON
4-2
Date
Class
Reteach
Angle Relationships in Triangles
According to the Triangle Sum Theorem, the sum of the angle
measures of a triangle is 180°.
*
—
m⬔J ⫹ m⬔K ⫹ m⬔L ⫽ 62 ⫹ 73 ⫹ 45
⫽ 180°
,
The corollary below follows directly from the Triangle Sum Theorem.
Corollary
—
—
+
Example
The acute angles of a right
triangle are complementary.
m⬔C ⫽ 90 ⫺ 39
⫽ 51°
#
—
%
$
m⬔C ⫹ m⬔E ⫽ 90°
Use the figure for Exercises 1 and 2.
1. Find m⬔ABC.
!
47°
—
2. Find m⬔CAD.
$
38°
—
—
"
#
Use 䉭RST for Exercises 3 and 4.
2
3. What is the value of x?
X—
14
X—
4. What is the measure of each angle?
m⬔R ⫽ 85°; m⬔S ⫽ 30°; m⬔T ⫽ 65°
4
X—
3
What is the measure of each angle?
7
!
-
—
,
—
.
5. ⬔L
"
5
#
6. ⬔C
49°
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
X—
6
7. ⬔W
39.8°
14
(90 ⫺ x)°
Holt Geometry
Name
Date
Class
Reteach
LESSON
4-2
Angle Relationships in Triangles
An exterior angle of a triangle is formed by
one side of the triangle and the extension of
an adjacent side.
continued
remote
interior angles
exterior
angle
⬔1 and ⬔2 are the remote interior angles of
⬔4 because they are not adjacent to ⬔4.
Exterior Angle Theorem
The measure of an exterior angle of a
triangle is equal to the sum of the
measures of its remote interior angles.
m⬔4 ⫽ m⬔1 ⫹ m⬔2
Third Angles Theorem
If two angles of one triangle are congruent
to two angles of another triangle, then
the third pair of angles are congruent.
Find each angle measure.
&
$
X—
—
—
*
#
'
(
8. m⬔G
X —
—
"
!
9. m⬔D
51°
41°
Find each angle measure.
,
.
5
0
X—
X—
1
X—
4
+
X —
-
10. m⬔M and m⬔Q
2
11. m⬔T and m⬔R
82°; 82°
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
3
33°; 33°
15
Holt Geometry