# Angle Pairs: Types of angle pairs

#### Academic Questions in MathematicsPlease check out our Test Your Knowledge page to see all Questions and Answers Factorize 12a2 - 20a + 3 A. (6a - 1)(2a - 3) B. (6a - 1)(2a + 3) C. (6a + 1)(2a - 3) D. (6a + 1)(2a + 3) E. (-6a + 1)(2a - 3) F. (-6a + 1)(2a + 3) Simplify 10ab + 7ab A. 17ab2 B. 17a2b2 C. 3ab2 D. 3a2b2 E. 17ab F 3ab Which of the following is not a type of angle? A. Right angle B. Left Angle C. Acute Angle D. Complete Angle E. Straight Angle F. Reflex angle Two lines that can never meet each other are best considered as _____ lines. A. straight B. vertical C. horizontal D. parallel E. oblique F. perpendicular An angle at exactly 90o is a/an _____ angle. A. acute B. obtuse C. reflex D. right E. complete F. straight Slanted or tilted lines that will finally meet at some point but NOT at a right angle are referred to as _____. A. Oblique B. Curved C. Vertical D. Perpendicular E. Parallel F. Horizontal The two sides that forms an angle are referred to as the _____. A. Arms B. Vertexes C. Bays D. Zones E. Limbs F. Dune The point where the two sides of an angle meet is termed the _____. A. Arms B. Vertex C. Bays D. Zones E. Limbs F. Dune ### Types of angle pairs:

An angle is a figure formed when the two sides of a line (termed rays) meet at the vertex. Recall that the vertex is a common endpoint where the two sides of a line (rays or arms) meet.

In geometry, we have a category of angles known as angle pairs (or pairs of angles). Such angles are described as angle pairs because they always occur in twos. Their occurrence in pair will also show a specific property in the respective angles.

Note: Recall that angles can also be classified based on their degree measurement.

Below are types or classifications of angles based on their occurrence in pairs:

1. Complementary Angles: These are two angles (or pair angles) that sum exactly to 90o. Understand that a 90o angle is also termed a right angle. For this reason, the 30o and 60o angles (sharing a common endpoint) will be considered as complementary angles because they sum up to a right angle (90o). They are shown in the image below: 2. Supplementary Angles: These are pair angles whose sum equals 180o. In the image below, notice that the angles (120o and 60o) are supplementary because they sum up to 180o. Recall that the 180o angle is also termed a straight angle or angle on a straight line.

3. Adjacent Angles: Two angles are said to be adjacent when they share the same arm and vertex which does not overlap. In the image below, notice that the three arms (or rays) of the angle do not overlap and they also meet at a common endpoint called the vertex. 4. Corresponding Angles: These are pair angles present on the same side of the vertex when a line intersects a pair of parallel lines. It is noteworthy to state that corresponding angles are always on the same side. See the image below: Corresponding angles are always equal to each other when the lines are parallel. However, the line that intersects both parallel lines is called the transversal.

5. Alternate Interior Angles: They are pair angles formed when a line intersects or cuts two parallel lines. The intersecting line is called the transversal. Alternate interior angles are in opposition to each other. Also, both alternating angles are always equal when the lines are parallel. The Alternate Interior Angles Theorem states that if two lines are parallel, then the pairs of alternate interior angles are congruent.

Note: The term congruent in the above theorem implies that both angles are equal, identical in form and coincides exactly when superimposed.

6. Alternate Exterior Angles: In simple terms, the alternate exterior angles are the vertical angles of the alternate interior angles. They are always equivalent or the same when the transversal intersects two parallel lines. They are shown in the image below: 7. Vertically Opposite Angle: These are angles formed at a point where two opposite lines cross or intersects each other centrally. The term vertical (in vertically opposite angles) implies that both angles share the same vertex; and not necessarily the common up-down meaning often ascribed to vertical.

The image below shows two pairs of vertically opposite angles. Notice that the sum of degree measurement in vertically opposite angles is always lesser than 360o with both angles having equal degree measurements. Vertically opposite angles may simple be referred to as vertical angles.

Instances where vertically opposite angles are present in real-life include a pair of open scissors, railroad crossing signs, open pliers, etc. Alfred Ajibola is a Medical Biochemist, a passionate Academician with over 7 years of experience, a Versatile Writer, a Web Developer, a Cisco Certified Network Associate and a Cisco CyberOps Associate.

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