Writing and Adding Angles
Main Learning Goal and Core Concepts: Students will be able to write and identify specific angles as well as add angles when given a missing angle.
Vocabulary
Ray
A line of indefinite length extending from an end point in one direction
Vertex
A point where two or more rays or the arms of an angle meet
Lesson Brief
How do we read angles?
 Like with other math problems, we use symbols to abbreviate what we are asked to do

 Example: x, ÷, +, , =
 With angles, we use the symbol “∠”

Example: Suppose we have a vertex like the following. How would we read it if we were asked to find angle B?
 We could label it as m∠B (“measurement of angle B”) or m∠ABC (“measurement of angle A, B, C [note how the B is in the middle]).
 The “m” lets us know that we are trying to find the degree angle of B.
 Note how this vertex can only have one angle that can be extracted.
How do we read angles in more complex situations?
Example:
 This can be a little more complex. We have a vertex where two different angles can be extracted.
 We have four different points, but we are focused on point B.
 So, how do we name both angles?
 ∠ABD or ∠DBA
 ∠CBD or ∠DBC
 Again, note how the B point is in the middle. This let’s us know that our main focus is B. Also, since we have two different angles here, it is important to include all points that are a part of the specific angle.
How do we add angles?
 If we are given the degrees of the angles, we simply add and make sure we include our degree symbol.
What if we are missing the degree of an angle in an addition problem?
 We can:
 look for symbols within the vertex (right angle/90°)
 use our previous knowledge of angles (180° = line, 360° = circle)
 use the surrounding angle degrees to find the missing angle
 look for keywords if we are dealing with a word problem
1. Find the missing angle:
2. Find the missing angle:
3. Find the missing angle:
4. Find m∠KLM if m∠KLB = 26° and m∠BLM = 60°
5. Find m<FGH if m∠FGB = 105 °and m∠BGH = 54°
6. Find m∠WDC if m∠EDC = 145° and m∠EDW = 61°
1. Find the missing angle:
Answer: 145°
Explanation: We are given the angle names so we know where each angle is. When we read the angles, we see that we will be adding to find the missing angle. We are also given the degrees of the angles we are adding, so we simply add 70° and 75° and get our answer of 145°.
2. Find the missing angle:
Answer: 40°
Explanation: When we read the angles, we see that we need to find the smaller angle of the vertex. Since we are given one of the angles and the angles total, we could subtract 115 ° from 155° and we get our answer of 40°.
3. Find the missing angle:
Answer: 51°
Explanation: Like our previous problem, we are also asked to find one of the angles. We are given one of the angles’ measurements and the total. So, to find the missing angle we can subtract 54° from 105° and get our answer of 51°.
4. Find m∠KLM if m∠KLB = 26° and m∠BLM = 60°
Answer: 86°
Explanation: Here, we are directly told which angle we need to find. We are essentially told to find the total of both angles. Since we are given the measurement of the two angles, we simply add 26° and 60° which gives us our answer of 86°.
5. Find m<FGH if m∠FGB = 105 °and m∠BGH = 54°
Answer: 159°
Explanation: Since we are told which angle’s measure we need to find, and we are told the measurements of the two other angles we simply add to get our answer. We add 105° and 54° and get our answer of 159°.
6. Find m∠WDC if m∠EDC = 145° and m∠EDW = 61°
Answer: 84°
Explanation: This problem is asking us to find the missing angle. We are given one of the angles measures as well as the total of both angles. With this information, we can simply subtract 61° (one of the given angles) from 145° (the total) and get our answer of 84°.
Notes:
 It is important to thoroughly read the angles and their measurements. Doing so helps us identify what angle(s) we are given and what angle(s) we need to find.
If you would like to look at additional examples, you can find them linked here and here.
‘Ray’ Definition: Source
Vertex’ Definition: Source
Download the blank and answer key worksheets below:
Writing and Adding Angles Worksheet
Writing and Adding Angles Answer Key