Download ExamView - 4.2 Triangle Sum Theorem Quiz.tst

Name: ________________________ Class: ___________________ Date: __________
ID: A
4.2 Triangle Sum Theorem Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find the measure of each numbered angle.
a.
b.
c.
d.
m∠1 = 54°, m∠2 = 117°, m∠3 = 63°
m∠1 = 117°, m∠2 = 63°, m∠3 = 63°
m∠1 = 54°, m∠2 = 63°, m∠3 = 63°
m∠1 = 54°, m∠2 = 63°, m∠3 = 117°
____
2. One of the acute angles in a right triangle has a measure of 34.6°. What is the measure of the other acute
angle?
a. 145.4°
b. 34.6°
c. 55.4°
d. 90°
____
3. Find m∠DCB, given ∠A ≅ ∠F , ∠B ≅ ∠E , and m∠CDE = 46°.
a.
b.
c.
d.
m∠DCB = 134°
m∠DCB = 67°
m∠DCB = 44°
m∠DCB = 46°
Short Answer
4. The degree measures of the angles of
ABC are represented by x, 3x, and 5x − 54. Find the value of x.
x = ____________________
1
ID: A
4.2 Triangle Sum Theorem Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: C
Step 1: ∠2 is supplementary to the angle that is 117°.
117° + m∠2 = 180°. So m∠2 = 63° .
Step 2: By the Alternate Interior Angles Theorem, ∠2 ≅ ∠3.
So m∠2 = m∠3 = 63° .
Step 3: By the Isosceles Triangle Theorem, ∠2 and the angle opposite the other side of the isosceles triangle
are congruent. Let ∠4 be that unknown angle.
Then, ∠2 ≅ ∠4 and m∠2 = m∠4 = 63° .
m∠1 + m∠2 + m∠4 = 180° by the Triangle Sum Theorem.
m∠1 + 63° + 63° = 180° . So m∠1 = 54° .
Feedback
A
B
C
D
Angle 2 is supplementary to the angle that measures 117 degrees.
To find the measure of angle 1, use the Isosceles Triangle Theorem.
Correct!
By the Alternate Interior Angles Theorem, angle 2 is congruent to angle 3.
PTS: 1
DIF: Advanced
REF: 1a9de092-4683-11df-9c7d-001185f0d2ea
STA: NY.NYLES.MTH.05.GEO.G.G.30 | NY.NYLES.MTH.05.GEO.G.G.36
LOC: MTH.C.11.03.02.04.002
TOP: 4-8 Isosceles and Equilateral Triangles
KEY: multi-step | isosceles triangle theorem
DOK: DOK 2
2. ANS: C
Let the acute angles be ∠M and ∠N , with m∠M = 34.6°.
m∠M + m∠N = 90°
The acute angles of a right triangle are complementary.
34.6° + m∠N = 90°
Substitute 34.6° for m∠M .
m∠N = 55.4°
Subtract 34.6° from both sides.
Feedback
A
B
C
D
The two acute angles in a right triangle are complementary.
This is the measure of the given angle. Find the measure of the other acute angle.
Correct!
The measure of the other acute angle is less than 90 degrees.
PTS:
OBJ:
TOP:
DOK:
1
DIF: Basic
REF: 1a6993ba-4683-11df-9c7d-001185f0d2ea
4-2.2 Finding Angle Measures in Right Triangles
LOC: MTH.C.11.03.02.05.001
4-2 Angle Relationships in Triangles
KEY: triangle sum theorem
DOK 1
1
ID: A
3. ANS: D
The Third Angles Theorem states that if two angles of one triangle are congruent to two angles of another
triangle, then the third pair of angles are congruent.
It is given that ∠A ≅ ∠F and ∠B ≅ ∠E . Therefore, ∠CDE ≅ ∠DCB. So, m∠DCB = 46°.
Feedback
A
B
C
D
This is the supplement. Use the Third Angles Theorem.
The Third Angles Theorem states that if two angles of one triangle are congruent to two
angles of another triangle, then the third pair of angles are congruent.
This is the complement. Use the Third Angles Theorem.
Correct!
PTS:
NAT:
TOP:
KEY:
1
DIF: Advanced
REF: 1a6e5872-4683-11df-9c7d-001185f0d2ea
NT.CCSS.MTH.10.9-12.G.SRT.5 LOC: MTH.C.11.03.02.04.005
4-2 Angle Relationships in Triangles
third angles theorem | triangle sum theorem
DOK: DOK 2
SHORT ANSWER
4. ANS:
26. x + 3x + 5x − 54 = 180
9x = 234
x = 26
PTS: 2
REF: 080933ge
STA: G.G.30
TOP: Interior and Exterior Angles of Triangles
2
Name: ________________________ Class: ___________________ Date: __________
ID: B
4.2 Triangle Sum Theorem Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. One of the acute angles in a right triangle has a measure of 18.4°. What is the measure of the other acute
angle?
a. 161.6°
b. 90°
c. 71.6°
d. 18.4°
____
2. Find the measure of each numbered angle.
a.
b.
c.
d.
____
m∠1 = 117°, m∠2 = 63°, m∠3 = 63°
m∠1 = 54°, m∠2 = 117°, m∠3 = 63°
m∠1 = 54°, m∠2 = 63°, m∠3 = 117°
m∠1 = 54°, m∠2 = 63°, m∠3 = 63°
3. Find m∠DCB, given ∠A ≅ ∠F , ∠B ≅ ∠E , and m∠CDE = 23°.
a.
b.
c.
d.
m∠DCB = 157°
m∠DCB = 67°
m∠DCB = 23°
m∠DCB = 78.5°
Short Answer
4. The degree measures of the angles of
ABC are represented by x, 3x, and 5x − 54. Find the value of x.
x = ____________________
1
ID: B
4.2 Triangle Sum Theorem Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: C
Let the acute angles be ∠M and ∠N , with m∠M = 18.4°.
m∠M + m∠N = 90°
The acute angles of a right triangle are complementary.
18.4° + m∠N = 90°
Substitute 18.4° for m∠M .
m∠N = 71.6°
Subtract 18.4° from both sides.
Feedback
A
B
C
D
The two acute angles in a right triangle are complementary.
The measure of the other acute angle is less than 90 degrees.
Correct!
This is the measure of the given angle. Find the measure of the other acute angle.
PTS: 1
DIF: Basic
REF: 1a6993ba-4683-11df-9c7d-001185f0d2ea
OBJ: 4-2.2 Finding Angle Measures in Right Triangles
LOC: MTH.C.11.03.02.05.001
TOP: 4-2 Angle Relationships in Triangles
KEY: triangle sum theorem
DOK: DOK 1
2. ANS: D
Step 1: ∠2 is supplementary to the angle that is 117°.
117° + m∠2 = 180°. So m∠2 = 63° .
Step 2: By the Alternate Interior Angles Theorem, ∠2 ≅ ∠3.
So m∠2 = m∠3 = 63° .
Step 3: By the Isosceles Triangle Theorem, ∠2 and the angle opposite the other side of the isosceles triangle
are congruent. Let ∠4 be that unknown angle.
Then, ∠2 ≅ ∠4 and m∠2 = m∠4 = 63° .
m∠1 + m∠2 + m∠4 = 180° by the Triangle Sum Theorem.
m∠1 + 63° + 63° = 180° . So m∠1 = 54° .
Feedback
A
B
C
D
To find the measure of angle 1, use the Isosceles Triangle Theorem.
Angle 2 is supplementary to the angle that measures 117 degrees.
By the Alternate Interior Angles Theorem, angle 2 is congruent to angle 3.
Correct!
PTS:
STA:
LOC:
KEY:
1
DIF: Advanced
REF: 1a9de092-4683-11df-9c7d-001185f0d2ea
NY.NYLES.MTH.05.GEO.G.G.30 | NY.NYLES.MTH.05.GEO.G.G.36
MTH.C.11.03.02.04.002
TOP: 4-8 Isosceles and Equilateral Triangles
multi-step | isosceles triangle theorem
DOK: DOK 2
1
ID: B
3. ANS: C
The Third Angles Theorem states that if two angles of one triangle are congruent to two angles of another
triangle, then the third pair of angles are congruent.
It is given that ∠A ≅ ∠F and ∠B ≅ ∠E . Therefore, ∠CDE ≅ ∠DCB. So, m∠DCB = 23°.
Feedback
A
B
C
D
This is the supplement. Use the Third Angles Theorem.
This is the complement. Use the Third Angles Theorem.
Correct!
The Third Angles Theorem states that if two angles of one triangle are congruent to two
angles of another triangle, then the third pair of angles are congruent.
PTS:
NAT:
TOP:
KEY:
1
DIF: Advanced
REF: 1a6e5872-4683-11df-9c7d-001185f0d2ea
NT.CCSS.MTH.10.9-12.G.SRT.5 LOC: MTH.C.11.03.02.04.005
4-2 Angle Relationships in Triangles
third angles theorem | triangle sum theorem
DOK: DOK 2
SHORT ANSWER
4. ANS:
26. x + 3x + 5x − 54 = 180
9x = 234
x = 26
PTS: 2
REF: 080933ge
STA: G.G.30
TOP: Interior and Exterior Angles of Triangles
2
Name: ________________________ Class: ___________________ Date: __________
ID: C
4.2 Triangle Sum Theorem Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find the measure of each numbered angle.
a.
b.
c.
d.
m∠1 = 54°, m∠2 = 63°, m∠3 = 63°
m∠1 = 117°, m∠2 = 63°, m∠3 = 63°
m∠1 = 54°, m∠2 = 117°, m∠3 = 63°
m∠1 = 54°, m∠2 = 63°, m∠3 = 117°
____
2. One of the acute angles in a right triangle has a measure of 37.2°. What is the measure of the other acute
angle?
a. 52.8°
b. 90°
c. 37.2°
d. 142.8°
____
3. Find m∠DCB, given ∠A ≅ ∠F , ∠B ≅ ∠E , and m∠CDE = 24°.
a.
b.
c.
d.
m∠DCB = 24°
m∠DCB = 156°
m∠DCB = 78°
m∠DCB = 66°
Short Answer
4. The degree measures of the angles of
ABC are represented by x, 3x, and 5x − 54. Find the value of x.
x = ____________________
1
ID: C
4.2 Triangle Sum Theorem Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: A
Step 1: ∠2 is supplementary to the angle that is 117°.
117° + m∠2 = 180°. So m∠2 = 63° .
Step 2: By the Alternate Interior Angles Theorem, ∠2 ≅ ∠3.
So m∠2 = m∠3 = 63° .
Step 3: By the Isosceles Triangle Theorem, ∠2 and the angle opposite the other side of the isosceles triangle
are congruent. Let ∠4 be that unknown angle.
Then, ∠2 ≅ ∠4 and m∠2 = m∠4 = 63° .
m∠1 + m∠2 + m∠4 = 180° by the Triangle Sum Theorem.
m∠1 + 63° + 63° = 180° . So m∠1 = 54° .
Feedback
A
B
C
D
Correct!
To find the measure of angle 1, use the Isosceles Triangle Theorem.
Angle 2 is supplementary to the angle that measures 117 degrees.
By the Alternate Interior Angles Theorem, angle 2 is congruent to angle 3.
PTS: 1
DIF: Advanced
REF: 1a9de092-4683-11df-9c7d-001185f0d2ea
STA: NY.NYLES.MTH.05.GEO.G.G.30 | NY.NYLES.MTH.05.GEO.G.G.36
LOC: MTH.C.11.03.02.04.002
TOP: 4-8 Isosceles and Equilateral Triangles
KEY: multi-step | isosceles triangle theorem
DOK: DOK 2
2. ANS: A
Let the acute angles be ∠M and ∠N , with m∠M = 37.2°.
m∠M + m∠N = 90°
The acute angles of a right triangle are complementary.
37.2° + m∠N = 90°
Substitute 37.2° for m∠M .
m∠N = 52.8°
Subtract 37.2° from both sides.
Feedback
A
B
C
D
Correct!
The measure of the other acute angle is less than 90 degrees.
This is the measure of the given angle. Find the measure of the other acute angle.
The two acute angles in a right triangle are complementary.
PTS:
OBJ:
TOP:
DOK:
1
DIF: Basic
REF: 1a6993ba-4683-11df-9c7d-001185f0d2ea
4-2.2 Finding Angle Measures in Right Triangles
LOC: MTH.C.11.03.02.05.001
4-2 Angle Relationships in Triangles
KEY: triangle sum theorem
DOK 1
1
ID: C
3. ANS: A
The Third Angles Theorem states that if two angles of one triangle are congruent to two angles of another
triangle, then the third pair of angles are congruent.
It is given that ∠A ≅ ∠F and ∠B ≅ ∠E . Therefore, ∠CDE ≅ ∠DCB. So, m∠DCB = 24°.
Feedback
A
B
C
D
Correct!
This is the supplement. Use the Third Angles Theorem.
The Third Angles Theorem states that if two angles of one triangle are congruent to two
angles of another triangle, then the third pair of angles are congruent.
This is the complement. Use the Third Angles Theorem.
PTS:
NAT:
TOP:
KEY:
1
DIF: Advanced
REF: 1a6e5872-4683-11df-9c7d-001185f0d2ea
NT.CCSS.MTH.10.9-12.G.SRT.5 LOC: MTH.C.11.03.02.04.005
4-2 Angle Relationships in Triangles
third angles theorem | triangle sum theorem
DOK: DOK 2
SHORT ANSWER
4. ANS:
26. x + 3x + 5x − 54 = 180
9x = 234
x = 26
PTS: 2
REF: 080933ge
STA: G.G.30
TOP: Interior and Exterior Angles of Triangles
2