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Name _______________________________________ 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
__________________
For Exercises 4–7, fill in the blanks to complete each theorem or corollary.
4. The measure of each angle of an _______________ triangle is 608.
5. The sum of the angle measures of a triangle is _______________.
6. The acute angles of a _______________ triangle are complementary.
7. The measure of an _______________ of a triangle is equal to the sum
of the measures of its remote interior angles.
Find the measure of each angle.
8. mB ___________________
9. mF __________________
10. mG ___________________
11. mL ___________________
12. mP ___________________
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.
________________________________________
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Holt McDougal Geometry
Name _______________________________________ Date __________________ Class __________________
Practice C
11. 7; 7; 4
1. 228 ft 8 in.
2. 83 ft 2 in.
Challenge
3. For ABC, x  1 or 1 because the
triangles are isosceles, x2  1, so x 
1. For DEF, x  1 because a length
cannot be negative, and if x  1 then
EF  1. So x  1 is the only solution for
DEF.
4. ABC must be isosceles and DEF
must be an equilateral triangle.
5. GH  GI  25, HI  9; GH  GI  9, HI 
1
6. Possible answer: By the Corr. Angles
Postulate, mA = m21 = m23  60°
and mG  m14  m24  60.
Construct a line parallel to CE through
D. Then also by the Corr. Angles
Postulate, mD  m22  m1 
m15  m12  60. By the definition
of a straight angle and the Angle Add.
Postulate, m1 + m4 + m21  180,
but m1  m21  mA  60.
Therefore by substitution and the Subt.
Prop. of Equality, m4  60. Similar
reasoning will prove that m11  m18
 m19  60. By the Alt. Int. Angles
Theorem, m19  m20 and m18 
m16. m20  m10 and m16 
m5 by the Vertical Angles Theorem.
By the Alt. Int. Angles Theorem, m4 
m2 and m5  m7 and m10 
m8 and m11  m13. By the
definition of a straight angle, the Angle
Addition Postulate, substitution, and the
Subt. Prop., m17  m6  m3 
m9. Substitution will show that the
measure of every angle is 60 .
Because every angle has the same
measure, all of the angles are
congruent by the definition of congruent
angles.
1. 16
3. 3
5. 27
2. 7
4. 1
6. 21
 57
7.
8.  12
9.
 21
10.
 36
11.
Answers will vary.
Problem Solving
1. 3 frames
2. 4
3
3
1
ft; 4 ft; 5 ft
8
8
4
3. Santa Fe and El Paso, 427 km; El Paso
and Phoenix, 561 km; Phoenix and
Santa Fe, 609 km
4. scalene
5. B
6. J
Reading Strategies
1. scalene, obtuse
2. equilateral, equiangular, acute
3. isosceles, right
4. isosceles triangle
5. no such triangle
6. scalene right triangle
ANGLE RELATIONSHIPS IN
TRIANGLES
Reteach
1.
3.
5.
7.
9.
right
acute
acute
isosceles
isosceles
2.
4.
6.
8.
10.
obtuse
right
obtuse
scalene
9; 9; 9
Practice A
1. 1, 4, 6
2. 2, 3
3. 2, 3, 5
4. equiangular
5. 180
6. right
7. exterior angle
8. 115°
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Holt McDougal Geometry
Name _______________________________________ Date __________________ Class __________________
9. 70°
10. 60°
11. 65°
12. 35
13. 120°
14. 110°
Practice B
2. 45°
3. 45.1°
5. 89.7°
4. z°
6. 60°
7. 47°
8. 33°; 66°; 81°
11. 55°
47°
2. 38°
14
mR  85°; mS  30°; mT  65°
49°
6. 39.8°
7. (90  x)°
9. 41°
11. 33°; 33°
1. 101.1°
9. 44°; 44°
1.
3.
4.
5.
8. 51°
10. 82°; 82°
Challenge
10. 108°; 108°
1. 39°
12. 54°; 72°; 54°
3. Through C, draw line  || BA . So  is
also || DE. Then apply the Alt. Int. 
Thm. twice, followed by the  Add.
Post. x°  55°  62°  117°.
Practice C
2. 88°
1. Possible answer:
Statements
Reasons
1. Quadrilateral ABCD
1. Given
2. Draw AC.
2. Construction
3. mD  mDAC  mDCA  3. Triangle Sum
Thm.
180°, mB  mBAC 
mBCA  180°
4. Additional Answer: Proofs will vary.
Given: ABC with exterior angle
BCD
Prove: mBCD  m1  m2
Proof:
4. mD  mDAC  mDCA  4. Add. Prop. of 
mB  mBAC  mBCA 
360°
5. mDAC  mBAC 
mDAB, mDCA  mBCA
 mDCB
5. Angle Add.
Post.
6. mD  mDAB  mB 
mDCB  360°
6. Subst.
Statements
2.
3. 360
4. interior  540°; exterior  360°
5. x  93; y  52; z  35
Reteach
Reasons
1. ABC with
exterior angle
BCD
1. Given
2. Through C, draw
line  parallel to
AB .
2. Through a point
outside a line, there is
exactly one line
parallel to the given
line.
3. m1  m3
3.  lines  corr. s 
4. m2  m4
4.  lines  alt. int. s 
5. mBCD  m3 
m4
5.  Add. Post.
6. mBCD  m1 
m2
6. Subst. Prop. of 
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry