Interior Angle Sum of Triangles

Math 2 U3 D8 Triangle & Polygon Review

By MARION MILLICAN

​Types of Triangles

Multiple Choice

Which type of triangle is pictured?

• Equilateral Triangle
• Right Isosceles Triangle
• Obtuse Scalene Triangle
• Obtuse Equilateral Triangle

Multiple Choice

Look at the sides and angles of this triangle. Which type of triangle is pictured?

• Equilateral Triangle
• Scalene Triangle
• Isosceles Triangle
• Right Triangle

Multiple Choice

If a triangle has one angle greater than 90° and no equal sides, what type of triangle is it?

• Acute Isosceles
• Acute Scalene
• Obtuse Scalene
• Obtuse Isosceles

​The sum of the interior angles of a triangle is 180 degrees.

​x + 68 + 50 = 180

​

x + 118 = 180

​

x = 180 - 118

​

x = 62​

Multiple Choice

Find the measure of angle V.

• 65

• 130

• 60

• 50

Multiple Choice

Find the value of x.

• 180

• 30

• 60

• 90

Multiple Choice

Find the value of x.

• 24

• 93

• 150

• 30

Multiple Choice

Solve for x THEN find the degrees for angle A.

• 44^o
• 96^o
• -14^o
• 63^o

​Isosceles Triangle

​Equilateral Triangle

Multiple Choice

• 72
• 67
• 65
• 54

Multiple Choice

• 12
• 11
• 8
• 6

Multiple Choice

What is the value of x?

• 51
• 49
• 78

Multiple Choice

Use the Isosceles Triangle Theorem to find the value of x.

• -7

• -8

• -12

• 6

Multiple Choice

Find x

• 60
• 48
• 30
• 28

Polygons

• Regular : All sides and angles are Congruent

• Irregular : Any polygon that is not Regular.

• Concave : A line that contains a side passes outside the polygon.

• Convex : No line that contains a side passes through the polygon.

Multiple Choice

The name for this type of polygon is

• Quadrilateral

• Pentagon

• Hexagon

• Heptagon

• Octagon

Multiple Choice

What is a regular polygon?

• Polygon with all sides congruent
• Polygon with all angles congruent
• Polygon with all sides and angles congruent
• Polygon with no sides or angles congruent

Multiple Select

Which of the following shapes are not polygons?

Finding the Interior Angle Sum

Find the Interior Angle Sum of a Pentagon

Multiple Choice

Find the Interior Angle Sum of a Hexagon

• 360

• 720

• 1080

• 1260

Multiple Choice

Find the Interior Angle Sum of an Octagon

• 360

• 720

• 1080

• 1260

Find the Measure of One Interior Angle

Find the Measure of an Interior Angle in a Regular Pentagon

Multiple Choice

Find the measure of an interior angle in a regular hexagon.

• 60

• 120

• 135

• 90

Solving for the missing angle!

• To solve for the missing angle follow these steps!

• 1) Count the number of sides on the polygon - here we have 5 sides (pentagon)

• 2) Use our formula for the sum of the interior angles - S = 180(n - 2) S = 180(5-2) = 540 degrees

• 3) Add up the existing angles - 87 + 105 + 135 + 92 = 419 degrees

• 4) Subtract the sum of the existing angles from the sum of the interior angles : 540 - 419 = 121 degrees

Fill in the Blank

What the measure of the missing angle X?

Exterior Angles

Remember : the sum of the exterior angles for any polygons is always 360 degrees!

Fill in the Blank

What is the measure of each exterior angle of a regular decagon (10 sides) ?

*Hint* Regular means all of the sides and all of the angles are equal, including the exterior angles.

Fill in the Blank

What is the value of x?

*Hint* You need to add the values together and set them equal to the sum of the exterior angles.

Multiple Choice

Find the missing angle.

• 75

• 105

• 100

• 70

Multiple Choice

What is the sum of exterior angles of a pentagon?

• 180
• 360
• 540
• 760

Triangle Inequality Theorem states that the sum of any two side lengths of a triangle is greater than the third side length.

• In other words, add the two smallest side lengths of a triangle and compare it to the third side length. If the sum is greater than the third side length, then yes a triangle is possible if not then a triangle is not possible.

• For example, 7, 15, 17 makes a triangle since 7 + 15 > 17

• For example, 1, 2, 3 does not make a triangle since 1 + 2 is not greater than 3.

Multiple Select

Which of the following sets of side lengths will make a triangle?

• 7, 15, 17

• 8, 12, 16

• 3, 5, 10

• 4, 5, 10

• 22, 11, 11

Determining the possible values for a third side length of a triangle given two of the side lengths.

• First calculate the difference of the two given side lengths

• Second calculate the sum of the two given side lengths

• Combine the two values as a compound inequality, for example difference < x < sum

Multiple Choice

What is the range of possible values for x?

• 6 < x < 12

• 3 < x < 9

• 6 < x < 9

• 3 < x < 12

Ordering a Triangle's Angle measures given its Side Lengths

• The smallest angle is across from the shortest side.

• The largest angle is across from the longest side.

Multiple Choice

Order the angles from least to greatest.

• A, B, C

• C, B, A

• B, A, C

• B, C, A

Multiple Choice

Order the angles from least to greatest.

• A, B, C

• B, A, C

• A, C, B

• C, A, B

Ordering a Triangle's Side Lengths given its Angle Measure

• Shortest side will be across the smallest angle.

• Longest side will be across the largest angle.

Multiple Choice

Order the sides from least to greatest.

• AB, BC, CA

• BC, AB, CA

• AB, AC, BC

• CA, AB, BC

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS
• SAS
• ASA
• Not Possible

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS
• SAS
• ASA
• AAS

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS
• SAS
• ASA
• AAS

Multiple Choice

Which method will not prove triangles are congruent?

• ASA

• SAS

• SSA

• AAS

Multiple Choice

What does CPCTC stand for?

• Congruent parts of congruent triangles are congruent
• Corresponding parts of congruent triangles are congruent
• Corresponding parts of corresponding triangles are corresponding
• Corresponding parts of congruent triangles are Canadian.

Multiple Choice

If ΔABC ≅ ΔXYZ, which statement is always true?

• AB = AZ
• ∠B ≅ ∠Y
• ∠X ≅ ∠C
• AC = XC

Multiple Choice

What additional information is required to say these two triangles are congruent by ASA?

• DE ≅ LJ

• <F ≅ <L

• FE ≅ LK

• DE ≅ JK