Example applications of theorems

Given: Find: , , and

123 4

m

n

Given: Find: , , and and are vertical angles and therefore congruent

m

n

123 4

Given: Find: , , and and are vertical angles and therefore congruent

and form a linear pair, so they are supplementary

m

n

123 4

Given: Find: , , and and are vertical angles and therefore congruent

and form a linear pair, so they are supplementary

and are vertical angles and therefore congruent

m

n

123 4

Given: and Find: and

123 4

m

n

Given: and Find: and and form a linear pair, so they are supplementary 12

3 4m

n

Given: and Find: and and form a linear pair, so they are supplementary

Substituting with the given expressions:

123 4

m

n

Given: and Find: and and form a linear pair, so they are supplementary

Substituting with the given expressions:

Simplify:

123 4

m

n

Given: and Find: and and form a linear pair, so they are supplementary

Substituting with the given expressions:

Simplify:

Solve for x:

123 4

m

n

Given: and Find: and and form a linear pair, so they are supplementary

Substituting with the given expressions:

Simplify:

Solve for x:

123 4

m

n

Given: and Find: and and form a linear pair, so they are supplementary

Substituting with the given expressions:

Simplify:

Solve for x:

Substitute to find

123 4

m

n

Given: and Find: and and form a linear pair, so they are supplementary

Substituting with the given expressions:

Simplify:

Solve for x:

Substitute to find

123 4

m

n