Triangle Angle Theorems Answers

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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
2
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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
3

A triangle with exterior angles is shown. A horizontal line intersects with a diagonal line. Another line connects the horizontal line to the diagonal line to form a triangle. The exterior angle at the top left of the triangle is 130 degrees. The exterior angle at the top right of the triangle is x degrees. The exterior angle at the bottom of the triangle is 134 degrees.

Question illustration
A
84
B
96
C
132
D
264
4

A triangle with exterior angles is shown. A triangle sits on a line and forms 2 exterior angles on the left and right of the triangle of (2 h) degrees. The top interior angle of the triangle is 40 degrees.

Question illustration
A
h = 20
B
h = 35
C
h = 55
D
h = 70
5

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
6

Triangle X Y Z is shown.

Question illustration
A
m∠Y = 26°
B
m∠Y = 34°
C
m∠Y = 60°
D
m∠Y = 120°
7

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
8

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°
9

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.
10

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

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