Finding the Missing Angle in a Triangle

Created by Kristin King, Desert Willow12-30-10

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 1Draw a right triangle.

B

CALabel each angle.

Cut out the triangle.

Step 2Cut off the angles as

shown.

B

A C

Step 3Place the angles together

at a point to form a straight line.

AB

C

AB

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

So: 80º + 45º + ? º = 180ºIt’s an equation!

125º + ?º = 180ºStep 1: Add 80º + 45º

Step 2: Subtract 125º from both sides

?º = 55º Answer!

80º 45º

?

Check: 80º + 45º + 55º = 180º√

Lets try another:

32º

24º

?º

32º + 24º + ?º = 180ºStep 1: Add 32º + 24º

56º + ?º = 180ºStep 2: Subtract 56º from both sides

?º = 124º Answer!

Check: 32º + 24º + 124º = 180º√

This one is a bit tricky...but I think you can do it!!!

45º

?º

Hmmm....this one has a 45º angle, a mystery angle, and

an angle with a square corner.

When you remember what that square

corner means, put your finger by your

nose.(Remember: no nose

picking allowed!)Yes! The square corner means that it is a right angle.

I know that a right angle is equal to 90.º

45º

?º

So... 45º + 90º + ?º = 180ºStep 1: Add 45º + 90º

135º + ?º = 180ºStep 2: Subtract 135º from both sides

?º = 45º Answer!

Check: 45 + 90º + 45º = 180º√

Try a few on your own!

75º 52º

?º ?º = 53º

? = 35º55º

?º

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