Triangle and Exterior Angle Theorem

Exterior Angles of Triangles

Dr. Tom Giles

Angle Relationships in Triangles

Holt Geometry

Holt McDougal Geometry

An auxiliary line is a line that is added to a figure
to aid in a proof.

An auxiliary line

used in the

Triangle Sum

Theorem

Multiple Choice

Find the measure of the indicated angle.

• $$135\degree$$  

• $$55\degree$$  

• $$45\degree$$  

• $$60\degree$$  

Multiple Choice

Find the measure of the indicated angle.

• $$30\degree$$  

• $$25\degree$$  

• $$155\degree$$  

• $$65\degree$$  

All angles that form a straight line add up to 180°

An auxiliary line

used in the

Triangle Sum

Theorem

A corollary is a theorem whose proof follows
directly from another theorem. Here are two
corollaries to the Triangle Sum Theorem.

Multiple Choice

The angles inside an equilateral triangle are all ...

• 20 degrees

• 50 degrees

• 60 degrees

• 45 degrees

The interior is the set of all points inside the
figure. The exterior is the set of all points
outside the figure.

Interior

Exterior

An interior angle is formed by two sides of a
triangle. An exterior angle is formed by one
side of the triangle and extension of an adjacent
side.

∠4 is an exterior angle.

∠3 is an interior angle.

Interior

Exterior

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

What is the measure of x?

• 14

• 156

• 95

• 109

Each exterior angle has two remote interior angles. A
remote interior angle is an interior angle that is not
adjacent to the exterior angle.

Exterior

∠4 is an
exterior angle.

The remote
interior angles
of ∠4 are ∠1
and ∠2.

Multiple Choice

Find the measure of each angle indicated.

• $$70\degree$$

• $$170\degree$$

• $$10\degree$$

• $$40\degree$$

Multiple Choice

What is the measure of angle x?

• 70

• 160

• 135

• 20

Multiple Choice

Solve for x

• 60

• 120

• 40

• 65

Fill in the Blanks

Multiple Choice

Choose a correct equation to find x.

• 4x - 2 + 12x + 1 = 75

• 4x - 2 + 75 = 12x + 1

• 4x - 2 + 75 + 12x + 1 = 180

• 4x - 2 - 75

Multiple Choice

What is the measure of angle b?

• 36^o

• 36

• 36 degrees

Multiple Choice

Solve for x

• 65

• 65 degrees

Fill in the Blanks