6th Grade - Many Types Of Angles

 
     
 
     
 
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6th
Geometry
Many Types of Angles
Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.
Know the definitions of different types of angles and angle relationships. Identify angles and their relationships when looking at geometric figures. Know that vertical angles are a pair of opposite angles formed by intersecting lines. They share a common vertex and are bounded by the same lines, but are opposite each other in location. Vertical angles have no sides in common and the same angle measure. Know that adjacent angles are a pair of angles that have the same vertex and share a common ray coming out of the vertex (common side). Understand that complementary angles are two angles that share a vertex and the sum of their angles is 90°. Know that supplementary angles are two angles whose measures add up to 180°
 

Sample Problems

(1)

In the figure, which angle is vertical to angle a?

(B)

(2)

What is the relationship between angles a and b, in the figure below?

(adjacent angles)

(3)

Identify the relationship of angles in the figure and describe why they can be classified as such.

(complementary angles, together they measure 90)

(4)

Identify the relationship of angles in the figure and describe why they can be classified as such.



(supplementary angles, together they measure 180)

(5)

Name the angle that is vertical to angle 2 in the figure.

(angle 4)

Learning Tips

(1)

Vertical angles are angles that are formed by intersecting (crossing) lines. They have no common sides and are equal in measure. In the figure below, angle A and angle B are vertical, as angle D is vertical to angle C. If you look closely at the figure you will see that both angle A and angle B have one line, this is showing how these angles are equal in measure. Also, angle D and angle C have two lines to show that these two angles have the same measure. It is important to understand that vertical angles are always across from one another, not next to one another.

(2)

Adjacent angles share one vertex (end point). They also have a common side. In the figure below angle A is adjacent to angle B, because they have a common vertex and the middle line is their common side.

(3)

Complementary angles come together to make one 90°, right angle. A right angle is easy to spot because it looks like a capital L. Right, 90° angles can be found everywhere. Where the floor meets the wall is one example of a 90° angle. The square shape at the bottom left of the figure is showing that the figure truly is a right angle. This is due to the fact that an 88° angle, for example, can look very close to a capital L. Before determining if two or more angles are complementary, you must be certain that you are truly looking at a right angle. It is important to remember that the right angle (L shape) can be turned in any direction. In other words, it may be turned upside down, to the left, etc…

(4)

Supplementary angles can be identified by two or more angles joining together to make a 180° angle. A 180° angle is also known as a straight angle. This type of angle is easy to identify because the two angles are connected to a straight line. In the figure below, we can see the straight angle as the common line underneath each angle. It is important to remember that the straight angle can be turned in a number of directions. It can be sideways, diagonal, etc… The direction or placement of the line does not matter, if it is a straight line, it is worth 180°.

(5)

Memorization of each geometric term is very important. There are a variety of ways to try to memorize these angle terms. Flash cards with angles drawn on one side and the academic term on the other side is one option. You may also want to come up with mnemonic devices to help memorize the terms. For example, complimentary angles measure 90 degrees together. A 90 degree angle can be shown by making an L shape with your thumb and pointer finger. Many people use this hand signal as a symbol for loser. You can use the phrase “compliment the loser” to help relate complementary angles to a right angle. Also, supplementary starts with an “s”, as does straight angle. This may help keep these two ideas together. The word adjacent, can sound like “add Jason”, which is someone’s neighbor’s name. This may help children remember that adjacent angles are neighbors. However, it’s important to remember that they live right next door and share a fence (line).

Extra Help Problems

(1)

Which term(s) could be used to describe angles ABD and DBC: vertical, adjacent, supplementary or complimentary? Explain.


(adjacent angles, they are next to one another, share the same vertex and share line BD.

(2)

Which term(s) could be used to describe angles IMJ and JMK: vertical, adjacent, supplementary or complimentary? Explain.


(adjacent, they share the same vertex and line MJ.)

(3)

Identify all angles that are adjacent to angle HMI.

(GMH, IMJ)

(4)

Angle x and angle y are an angle pair. They share a common vertex, but don’t have any sides in common. They have the same measure and are opposite one another. Use a vocabulary term to identify the angle pair described above.

(vertical angles)

(5)

Angle S and angle T are an angle pair. They share a common vertex and a common side. Angle S has a measure of 40°, and T 26°. Use a vocabulary term to identify the angle pair described above.

(adjacent angles)

(6)

Identify all vertical angles in the figure and explain.

(1 is vertical to 3; 4 is vertical to 2)

(7)

Angle X measures 60°, while angle Y measures 30°. What geometric term could be used to describe this angle pair? Explain.

(complementary, they measure 90 together)

(8)

Angle L measures 150° and angle M measures 30°. What geometric term could be used to describe this angle pair? Explain.

(supplementary, they measure 180 together)


(9)

Which term(s) could be used to describe angles 1 and 2: vertical, adjacent, supplementary or complimentary? Explain.


(complementary, they measure 90)

(10)

Which term(s) could be used to describe angles 6 and 7: vertical, adjacent, supplementary or complimentary? Explain.

(supplementary, they measure 180)

(11)

Identify all vertical and adjacent angles in the figure. Describe the difference between the two types of angles.

(vertical:a and b, d and c; adjacent: a with c and a with d; c with a and c with b; b with c and b with d; d with b and d with a)

(12)

Identify all angles that are supplementary to angle 6? Explain.


(7 and 5)

(13)

Identify and list all vertical angles in the figure.

(1 and 3; 2 and 4, 5 and 7; 6 and 8)

(14)

Identify all angles that are adjacent to angle SXY.

(SXQ and YXU)

(15)

Identify the angles that are supplementary to angle JXQ.

(JXY or QXS)

(16)

Identify two complimentary angles in the figure below.

(UXY and YXS)

(17)

Identify all angles that are adjacent to angle LEY. Explain how you know they are adjacent.

(LED, shares line LE and Vertex E and YES, shares line YE and vertex E)

(18)

Identify the angle that is vertical to angle LED. Describe the traits that make them vertical.

(YES, they are opposite one another and have the same measure.)

(19)

Identify the angle that is complementary to angle YES? Explain how you know.

(SEH, both angles together make a right angle)

(20)

Find and list all the adjacent and supplementary angles in the figure below. Underneath each pair of angles, justify your identifications by describing why the angle is supplementary or adjacent.

(Adjacent: ABS with SBV (shares vertex B and line SB), ABS with ABG (shares vertex B and line AB), SVB with ABS (see above), SVB with VBG (shares vertex B and line VB), VGB with SVB (see above), VGB with ABG (shares vertex B and line BG))

(21)

Draw a pair of complimentary angles. Describe why this angle pair can be identified as complimentary.

(both angles together measure 90)




(22)

Draw a pair of adjacent angles. Describe why this angle pair can be identified as adjacent.

(Both angles share a vertex and a line.)






(23)

Draw a pair of vertical angles. Describe why this angle pair can be identified as vertical.

(They are opposite one another and have the same angle measure.)






(24)

Draw a pair of supplementary angles. Describe why this angle pair can be identified as supplementary.

(They measure 180 together.)






(25)

Jason folded his paper into equal fourths from corner to corner. When he unfolded the paper he saw an X shape. How could Jason describe the angles and their relationships as pairs?

(The opposite angles are vertical. The angles that share a line and vertex are adjacent. The angles that come together to make 180 angles are supplementary.)

 

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