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There are some special relationships between "pairs" of angles. Adjacent Angles are two angles that share a common vertex, a common side, and no common interior points. (They share a vertex and side, but do not overlap.)
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| ∠1 and ∠2 are adjacent angles. ∠ABC and ∠1 are NOT adjacent angles.
(∠ABC overlaps ∠1.)
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A Linear Pair is two adjacent angles whose non-common sides form opposite rays.
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| ∠1 and ∠2 form a linear pair. The line through points A, B and C is a straight line. ∠1 and ∠2 are supplementary.
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| If two angles form a linear pair, the angles are supplementary.
A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary.
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| If two congruent angles form a linear pair, the angles are right angles.
If two congruent angles add to 180º, each angle contains 90º, forming right angles.
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Vertical Angles are two angles whose sides form two pairs of opposite rays (straight lines).
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| Vertical angles are located across from one another in the corners of the "X" formed by the two straight lines. ∠1 and ∠2 are vertical angles.
∠3 and ∠4 are vertical angles. Vertical angles are not adjacent.
∠1 and ∠3 are not vertical angles (they are a linear pair). Vertical angles are always equal in measure.
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| Vertical angles are congruent.
Vertical angles, such as ∠1 and ∠2, form linear pairs with the same angle, ∠4, giving m∠1 + m∠4 = 180 and m∠2 + m∠4 = 180. With substitution, m∠1 = m∠2 and they are congruent.
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Complementary Angles are two angles the sum of whose measures is 90º.
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| Complementary angles can be placed so they form perpendicular lines, or they may be two separate angles.
∠1 and ∠2 are complementary.
∠P and ∠Q are complementary.
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| Complements of the same angle, or congruent angles, are congruent.
If m∠a is complementary to the m∠b, and m∠c is complementary to m∠b, then
m∠a = m∠c. Consider m∠a = 60º, m∠b = 30º and m∠c = 60º.
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| The acute angles of a right triangle are complementary.
The sum of the angles in a triangle add to 180º. After subtracting 90º for the right angle, there are 90º left for the two acute angles, making them complementary.
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Supplementary Angles are two angles the sum of whose measures is 180º.
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| Supplementary angles can be placed so they form a linear pair (straight line), or they may be two separate angles.
∠1 and ∠2 are supplementary.
∠P and ∠Q are supplementary. The line through points A, B and C is a straight line.
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| Supplements of the same angle, or congruent angles, are congruent.
If m∠a is supplementary to the m∠b, and m∠c is supplementary to m∠b, then
m∠a = m∠c. Consider m∠a = 60º, m∠b = 120º and m∠c = 60º.
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Is 1 and 3 A linear pair?
∠1 and ∠3 are not vertical angles (they are a linear pair). Vertical angles are always equal in measure. Vertical angles are congruent.
Are angles 1 and 3 congruent to each other?
Angles 1 and 3 are vertical angles. They are congruent. This can be written as ∠1 ≅ ∠3. If ∠1 measures 120° , then ∠3 measures 120°.
What type of angle pair is 2 and 3?
A linear pair is a pair of adjacent angles formed when two lines intersect. In the figure, ∠1 and ∠2 form a linear pair. So do ∠2 and ∠3 , ∠3 and ∠4 , and ∠1 and ∠4 .
What type of angle pair is 1 and 2?
Types of Angle Pairs. Adjacent angles: two angles with a common vertex, sharing a common side and no overlap. Angles ∠1 and ∠2 are adjacent.