AnswersCA-Common Core Geometry DVHS Sem. 1Symmetry

Triangle Angle Theorems Answers

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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
2
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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
3

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°
4

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°
5

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
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

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.
8

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
9

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°
10

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°
11

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
12

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
13

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
14

Given: Lines y and z are parallel, and ABC forms a triangle.Prove: m∠5 + m∠2 + m∠6 = 180° Statements Reasons1.ABC is a triangle1.given2.y ∥ z2.given3.∠1 ≅ ∠5; ∠3 ≅ ∠63.?4.m∠1 = m∠5; m∠3 = m∠64.def. ≅5.m∠1 + m∠2 + m∠3 = m∠LAM5.∠ addition postulate6.m∠1 + m∠2 + m∠3 = 180°6.def. straight angle7.m∠5 + m∠2 + m∠6 = 180°7.substitutionWhich could be the missing reason in Step 3?

Question illustration
A
alternate interior angles are congruent
B
alternate exterior angles are congruent
C
vertical angles are congruent
D
corresponding angles are congruent
15

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
16

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
17

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
18

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
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

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

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