Isosceles Triangles 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
2
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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°
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

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 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 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
7

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°
8

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
9

Triangle X Y Z is shown.

Question illustration
A
m∠Y = 26°
B
m∠Y = 34°
C
m∠Y = 60°
D
m∠Y = 120°
10

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

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