2.1 Lesson 4 - Triangle Sum and Exterior Angle Theorems

Lesson 4 - Conjectures About Triangles

Learning Goals

• I can identify and find the measure of exterior angles of triangles.

• I can make conjectures about the sum of the interior angles of a triangle and its exterior angles.

​Objective: Is to apply the Triangle Sum Theorem and understand to solve the missing angle

Multiple Choice

Find the measure of each angle indicated.

• $$50\degree$$

• $$120\degree$$

• $$30\degree$$

• $$20\degree$$

Multiple Choice

Find the value of x in the diagram so that the angles form a linear pair

• 118

• 62

• 72

• 68

Multiple Choice

Which angle is a linear pair with $$\angle1$$  ?

• $$\angle2$$  

• $$\angle3$$  

• $$\angle4$$  

• $$\angle5$$  

• $$\angle6$$  

Multiple Choice

What type of angles are these?

• Adjacent Angles

• Linear Pair

• Complementary Angles

• Supplementary Angles

• Vertical Angles

Multiple Choice

what is the measure of this angle

• 90

• 180

• 120

• 360

-Works if you know two angles in a triangle...

-All sums of the angles of a triangle equals 180​

​Some text here about the topic of discussion.

​Triangle Sum THeorem

​

Multiple Choice

What is the measure of x?

• 101°

• 111°

• 121°

• 131°

Multiple Choice

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______. 

• 45°

• 90°

• 180°

• 360°

Multiple Choice

Find the indicated angle measure.

(What is ?)

• 85

• 78

• 95

• 110

Multiple Choice

If two angles in a triangle are $$45\degree$$  and $$\ 75\degree$$ , what is the measure of the third angle?

• $$75\degree$$  

• $$90\degree$$  

• $$60\degree$$  

• $$70\degree$$  

Multiple Choice

Find the indicated angle measure. 

(What is ?)

• $$5\degree$$

• $$165\degree$$

• $$65\degree$$

• $$60\degree$$

Multiple Choice

Find the measure of the indicated angle.

• $$135\degree$$  

• $$55\degree$$  

• $$45\degree$$  

• $$60\degree$$  

Fill in the Blank

How many degrees are in a triangle?

Multiple Choice

Find the measure of the indicated angle.

• $$30\degree$$  

• $$25\degree$$  

• $$155\degree$$  

• $$65\degree$$  

Multiple Choice

Find the measure of the indicated angle.

• $$45\degree$$  

• $$33\degree$$  

• $$123\degree$$  

• $$147\degree$$  

​Exterior angle Theorem

• Angle 50, 70, and x are interior angles

• Angles inside the triangle not adjacent

• are remote interior angles

• 50+70=120 add your remote interior angles to equal the exterior angle

• The exterior angle is 120

• x=60 and is linear pair to 120. 120+60=180​

Multiple Choice

What is the value of the missing angle?

• 90

• 100

• 20

• 120

Multiple Choice

What is the value of the missing angle?

• 105

• 80

• 55

• 25

Multiple Choice

How much is the value of X?

• 85

• 95

• 75

• 100

Multiple Choice

What is the value of the missing angle?

• 90

• 100

• 20

• 120

Multiple Choice

How many degrees is X?

• 65

• 70

• 90

• 55

Multiple Choice

Find the measure of the missing angles.

• A

• B

• C

• D

Multiple Choice

How many degrees is X?

• 37

• 47

• 7

• 90

Multiple Choice

What is the value of the missing angle?

• 105

• 80

• 55

• 25

Multiple Choice

Find the measure of $$\angle A$$  .

• 25 degrees

• 35 degrees

• 40 degrees

• 45 degrees

Multiple Choice

Find the measure of $$\angle A$$  .

• 25 degrees

• 35 degrees

• 40 degrees

• 45 degrees

Multiple Choice

Find the measure of $$\angle D$$  .

• 45 degrees

• 60 degrees

• 90 degrees

• 30 degrees

Fill in the Blank

Solve for x.

Fill in the Blank

Solve for x.