1. Finding the Missing Angle in a Triangle
Created by Kristin King, Desert Willow

2. What is a 2-D figure? How can it be drawn using a ruler or protractor?
Standard:
G5.4M.C1.PO1. Draw and label 2-dimensional figures given specific attributes including angle measure and side lengths.
Essential Questions:
What is a 2-D figure? How can it be drawn using a ruler or protractor?
Today I can determine the unknown measurement of an angle in a triangle.

3. Fact: All of the angles in any given triangle add up to 180.º
Don’t believe me???
Let me prove it to you!!!

4. Step 1 B Label each angle. A C Cut out the triangle.
Draw a right triangle.
Label each angle. A C
Cut out the triangle.

5. Cut off the angles as shown.
Step 2 B A C
Cut off the angles as shown.

6. Place the angles together at a point to form a straight line.
Step 3 A B C
Place the angles together at a point to form a straight line.

7. Therefore, the sum of all the angles in a triangle is equal to 180!ºB C
The angles placed together form a straight line.
A straight line or straight angle is equal to 180º.
Therefore, the sum of all the angles in a triangle is equal to 180!º

8. You can use this fact to find the missing angle in a triangle.
For example, lets say I have the following triangle:
80º
45º ?
I know the measurements of two of the angles, but the third one is a mystery. How do I find the measurement of that third angle?

9. Remember that all the angles in a triangle added together equal 180.º
80º
45º ?
So: 80º + 45º + ? º = 180º
It’s an equation!
Step 1: Add 80º + 45º
125º + ?º = 180º
Step 2: Subtract 125º from both sides
Answer!
?º = 55º
Check: 80º + 45º + 55º = 180º √

10. Step 2: Subtract 56º from both sides
32º
24º ?º
Lets try another:
32º + 24º + ?º = 180º
Step 1: Add 32º + 24º
56º + ?º = 180º
Step 2: Subtract 56º from both sides
Answer!
?º = 124º
Check: 32º + 24º + 124º = 180º √

11. I know that a right angle is equal to 90.º
This one is a bit tricky...but I think you can do it!!!
When you remember what that square corner means, put your finger by your nose.
(Remember: no nose picking allowed!)
45º ?º
Hmmm....this one has a 45º angle, a mystery angle, and an angle with a square corner.
Yes! The square corner means that it is a right angle.
I know that a right angle is equal to 90.º

12. Step 2: Subtract 135º from both sides
45º ?º
So º + 90º + ?º = 180º
Step 1: Add 45º + 90º
135º + ?º = 180º
Step 2: Subtract 135º from both sides
Answer!
?º = 45º
Check: º + 45º = 180º √

13. Try a few on your own! 55º ?º 75º 52º ?º ? = 35º ?º = 53º 111º 33º ?º
? = 36º

14. Closure:
On your slate write down the steps to finding the measurement of the missing angle in a triangle.