Finding the Missing Angle in a Triangle

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Presentation transcript:

Finding the Missing Angle in a Triangle Created by Kristin King, Desert Willow 12-30-10

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.

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

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.

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

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.

Therefore, the sum of all the angles in a triangle is equal to 180!º B 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

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?

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 √

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 √

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

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

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

Closure: On your slate write down the steps to finding the measurement of the missing angle in a triangle. http://world.std.com/~eshu/dbug/Jeopardy_Think_Music.mp3