Angle Sum & Exterior Angle Theorems

Angle Sum & Exterior Angle Theorems with Equilateral & Isosceles Triangles

​Dr. Tom Giles

Fill in the Blank

Solve for x.

Solve for x.

• 7x - 11 + 5x - 2 + 2x - 3 = 180

• 14x - 16 = 180

• 14x = 196

• x = 14

Solve for x.

• 2x + 1 + 90 + 5x + 5 = 180

• 7x + 96 = 180

• 7x = 84

• x = 12

Fill in the Blank

Solve for x.

Fill in the Blank

Solve for x.

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.

• $$135\degree$$  

• $$55\degree$$  

• $$45\degree$$  

• $$60\degree$$  

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

Poll

Are you understanding the math concepts from this lesson today?

Isosceles & Equilateral Triangles

Multiple Choice

What do you call the angles along the base of an isosceles triangle?

¿Cómo se llaman los ángulos a lo largo de la base de un triángulo isósceles?

• Legs

• Vertex Angle

• Base

• Base Angles

Hint: Since this is an equilateral triangle, all the sides are the same!!! That means we can set the expressions for our unknown sides equal to 10.

Hint: What do each of the angles of an equilateral triangle have to be?

Multiple Choice

What do the angles in an equilateral triangle measure?

• 30, 60, 90

• 60, 60, 60

• 45, 45, 90

• 35, 55, 90

Multiple Choice

The sides of an equilateral triangle have...

• different measures.

• equal angles

• equal measures.

• 60°.

Multiple Choice

Find x

• 3

• 4

• 2

• 10

Multiple Choice

What is the length of DF?

• 8

• 4

• 25

• 71

Hint: In an isosceles triangle, the two base angles are congruent. If you need to find the vertex angle, just remember what all three angles should add up to!

Hint: In an isosceles triangle, exactly two sides are congruent!

Fill in the Blank

From the last slide, what did you get for x and the segment measure? (type answers as x, segment measure)

Hint: Start by solving for y...remember the two base angles are congruent! Then, you can find x using your knowledge of what the three angles of a triangle should add up to!

Fill in the Blank

From the last slide, what did you get for x and y? (type answers as x, y)

Multiple Choice

If two sides of a triangle are congruent, then the _________________ opposite those sides are congruent.

• sides

• vertices

• angles

• measures

Multiple Choice

Find x

• 10

• 32

• 116

• 16

Multiple Choice

What is the measure of ∠S?

• 60⁰

• 52⁰

• 45⁰

• 36⁰

Multiple Choice

What is the measure of ∠A?

• 46

• 134

• 90

• 88

Multiple Choice

• A

• B

• C

• D

Poll

Are you understanding the math concepts from this lesson today?