AnswersIntegrated Math 2A - Mr. Katykhin 26Triangle Angle Theorems

4.5 Triangle Angle Theorems Answers

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Triangle N P O is shown. Line O N extends through point M to form exterior angle P N M. Angle N P O is 38 degrees. Angle P O N is 39 degrees. Exterior angle P N M is x degrees.

Question illustration
A
x > 38
B
x < 39
C
x < 77
D
x > 103
2
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A triangle is sitting on a horizontal line. The bottom left interior angle of the triangle is (9 + k) degrees. The exterior angle to the bottom left interior angle is (5 k minus 3) degrees.

Question illustration
A
k = 28
B
k = 29
C
k = 31
D
k = 42
3

A triangle is shown with a line extending from the bottom left point

Question illustration
A
An exterior angle is supplementary to the adjacent interior angle.
B
An adjacent interior angle is supplementary to a remote interior angle.
C
A remote interior angle is congruent to the exterior angle.
D
An exterior angle is supplementary to a remote interior angle.
4

Which statements are always true regarding the diagram? Select three options.

A
m∠5 + m∠3 = m∠4
B
m∠3 + m∠4 + m∠5 = 180°
C
m∠5 + m∠6 =180°
D
m∠2 + m∠3 = m∠6
E
m∠2 + m∠3 + m∠5 = 180°
5

Triangle R T S is sitting on a horizontal line. Line S R extends through point Q to form exterior angle T R Q. Angle R T S is (25 x) degrees. Angle T S R is (57 + x) degrees. Exterior angle T R Q is (45 x) degrees.

Question illustration
A
x = 2
B
x = 3
C
x = 33
D
x = 52
6

A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.

Question illustration
A
m∠5 + m∠6 = m∠1
B
m∠3 + m∠4 + m∠5 = 180°
C
m∠1 + m∠2 = 180°
D
m∠2 + m∠3 = m∠5
7

A triangle has a bottom left angle of (x + 15) degrees and a bottom right angle of (x degrees). 1 parallel and horizontal line sits at the top point of the triangle. Another parallel and horizontal line sits at the base of the triangle. The exterior angle to the bottom right angle of the triangle is (4 x minus 20) degrees.

Question illustration
A
x = 32
B
x = 36
C
x = 37
D
x = 40
8

Triangle Q R S is shown with exterior angles. Line R Q extends through point D. Line Q R extends through point E. Line Q S extends through point C.

Question illustration
A
∠RSC
B
∠SRE
C
∠DQS
D
∠QSR
9

Triangle X Y Z is shown. Line Z X is extended through point W to form exterior angle W X Y.

Question illustration
A
m∠WXY = m∠YXZ
B
m∠WXY < m∠YZX
C
m∠WXY + m∠YXZ = 180°
D
m∠WXY + m∠XYZ = 180°
10

Triangle K M L is shown. Line L K extends through point J to form exterior angle J K M.

Question illustration
A
m∠MKL + m∠MLK = m∠JKM
B
m∠KML + m∠MLK = m∠JKM
C
m∠MKL + m∠MLK = 180°
D
m∠JKM + m∠MLK = 180°
11

Triangle K M L is shown. Line L K extends through point J to form exterior angle J K M.

Question illustration
A
m∠MKL + m∠MLK = m∠JKM
B
m∠KML + m∠MLK = m∠JKM
C
m∠MKL + m∠MLK = 180°
D
m∠JKM + m∠MLK = 180°
12

Triangle A B C is shown with its exterior angles. Line B A extends through point D. Line A B extends through point E. Line A C extends through point F.

Question illustration
A
∠CBA
B
∠CBE
C
∠DAC
D
∠BCF
13

A triangle is shown with a line extending from the bottom left point

Question illustration
A
An exterior angle is supplementary to the adjacent interior angle.
B
An adjacent interior angle is supplementary to a remote interior angle.
C
A remote interior angle is congruent to the exterior angle.
D
An exterior angle is supplementary to a remote interior angle.
14

Triangle A B F is shown. Line B F is extended through point G. Line F A is extended through point C. A line is drawn from point A to point D. A line is drawn from point F to point E.

Question illustration
A
∠BAD
B
∠AFE
C
∠CAD
D
∠CAB
15

Triangle N P O is shown. Line O N extends through point M to form exterior angle P N M. Angle N P O is 38 degrees. Angle P O N is 39 degrees. Exterior angle P N M is x degrees.

Question illustration
A
x > 38
B
x < 39
C
x < 77
D
x > 103
16

Triangle Q R S is shown with exterior angles. Line R Q extends through point D. Line Q R extends through point E. Line Q S extends through point C.

Question illustration
A
∠RSC
B
∠SRE
C
∠DQS
D
∠QSR
17

Triangle X Y Z is shown. Line Z X is extended through point W to form exterior angle W X Y.

Question illustration
A
m∠WXY = m∠YXZ
B
m∠WXY < m∠YZX
C
m∠WXY + m∠YXZ = 180°
D
m∠WXY + m∠XYZ = 180°
18

Which statements are always true regarding the diagram? Select three options.

A
m∠5 + m∠3 = m∠4
B
m∠3 + m∠4 + m∠5 = 180°
C
m∠5 + m∠6 =180°
D
m∠2 + m∠3 = m∠6
E
m∠2 + m∠3 + m∠5 = 180°
19

Triangle X Y Z is shown.

Question illustration
A
m∠Y = 26°
B
m∠Y = 34°
C
m∠Y = 60°
D
m∠Y = 120°
20

Triangle Q R S is shown. Line R Q extends through point P. Angle Q S R is 35 degrees. Angle S R Q is 58 degrees. Exterior angle S Q P is x degrees.

Question illustration
A
x = 23
B
x = 35
C
x = 58
D
x = 93

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