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Use your understanding of complementary, supplementary, and alternate angles to find the missing angles in the figures below. For help, see this lesson on Angle Relationships. (Page 1 of 3)

1. Calculate the value of angle x and complete the sentence below to describe the relationship between the two angles.

example of two complementary angles

 

x =   30°  

The 60° angle and angle x are   complementary   angles.

 

2. Calculate the value of angle x and complete the sentence below to describe the relationship between the two angles.

example of two supplementary angles

 

x =   50°  

The 130° angle and angle x are   supplementary   angles.

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Page 2 of 3: For help, see this lesson on Angle Relationships.

3. Calculate the values of angles a, b, and c and complete the sentence that describes their relationship .

two intersecting lines with four angles marked

a =   155°  

b =   25°  

c =   155°  

Angles a and c are   opposite   angles.

4. Complete the table below to show the values of the missing angles and the basis for your calculations. (note: there may be more than one correct basis for each)

two parallel lines with a transversal
a = 105° because a = e (corresponding angles)
b = 75° because b = 180° - a (supplementary angles)
c = 105° because a = c (opposite angles)
d = 75° because d = b (opposite angles)
e = 105° because e = 105° (opposite angles).
f = 75° because f = 180° - e (supplementary angles)
h = 75° because h = 180° - 105° (supplementary angles)

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Page 3 of 3: For help, see this lesson on Angle Relationships.

5. Use what you know about the sum of the angles in a triangle together with the properties of supplementary angles to calculate the missing angles in the figure below.

 

truss-like figure with missing angles indictaed

 

a = 35° because 80° + 65° + a = 180° (supplementary angles)
a = 180° - 145°
b = 50° because 35° + 95° + b = 180° (sum of angles in a triangle)
b = 180° - 130°
c = 85° because c + 95° = 180° (supplementary angles)
d = 30° because 65° + 85° + c = 180° (sum of angles in a triangle)
d = 180° - 150°

 

 

 


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Related Resources

The various resources listed below are aligned to the same standard, (8G05) taken from the CCSM (Common Core Standards For Mathematics) as the Geometry Worksheet shown above.

Use informal arguments to establish facts about the angle sum and exterior angle ...

Page

Worksheets

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Understand congruence and similarity using physical models, transparencies, or geometry software

 

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