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ANGLES: COMPLEMENTARY, SUPPLEMENTARY,
VERTICAL and LINEAR PAIRS

Jump right to the exercises!

ASSUME ALL ANGLES ARE MEASURED IN DEGREES.

DEFINITION: complementary angles
Two angles are complementary iff their sum is 90° .

Note: If  ∠1  and  ∠2  are complementary, then m∠1+ m∠2 = 90° .

DEFINITION: supplementary angles
Two angles are supplementary iff their sum is 180° .

Note: If  ∠1  and  ∠2  are supplementary, then m∠1+ m∠2 = 180° .

DEFINITION: opposite rays
Rays that share a common endpoint and point in opposite directions are called opposite rays.

Note: If three points are on a line with  A-B-C , then  BA→  and  BC→  are opposite rays.

DEFINITION: linear pair
Two angles are a linear pair iff they have a common side and their other sides are opposite rays.

If  ∠1  and  ∠2  are a linear pair, then m∠1+ m∠2 = 180° .

DEFINITION: vertical angles
Two angles are vertical angles iff the sides of one angle are opposite rays to the sides of the other.

Note: Vertical angles are the "opposite angles" that are formed by two intersecting lines.
Note: If  ∠1  and  ∠2  are vertical angles, then m∠1= m∠2 .

DEFINITION: parallel lines
Two lines are parallel if and only if they lie in the same plane and do not intersect.

Note: The symbol  ∥  is used to denote parallel lines.
The sentence " l∥m " is read as " l  is parallel to  m ", and is true precisely when line  l  is parallel to line  m .

DEFINITION: perpendicular lines
Two lines are perpendicular if and only if they form a right angle.

Note: The symbol  ⊥  is used to denote perpendicular lines.
The sentence " l⊥m " is read as " l  is perpendicular to  m ", and is true precisely when line  l  is perpendicular to line  m .

SAMPLE PROBLEM:
Suppose that  ∠1  and  ∠2  are vertical angles.
Suppose that    m∠1= 7x-15   and    m∠2= 2x+55 .
Find  x .

SOLUTION:
7x-15= 2x+55(vertical angles have equal measures)
5x-15= 55 (subtract  2x  from both sides)
5x=70 (add  15  to both sides)
x=14 (divide both sides by  5 )

On this exercise, you will not key in your answers.
However, you can check to see if your answer is correct.
Click on "new problem" to get started!