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.

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A
x > 38
B
x < 39
C
x < 77
D
x > 103
3

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

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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°
4

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.

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A
x = 2
B
x = 3
C
x = 33
D
x = 52
5

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

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A
m∠WXY = m∠YXZ
B
m∠WXY < m∠YZX
C
m∠WXY + m∠YXZ = 180°
D
m∠WXY + m∠XYZ = 180°
6

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.

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A
∠RSC
B
∠SRE
C
∠DQS
D
∠QSR
7

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.

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A
x = 23
B
x = 35
C
x = 58
D
x = 93
8

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.

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A
∠BAD
B
∠AFE
C
∠CAD
D
∠CAB
9

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°
10

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

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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.

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