Interior and Exterior Angels of Triangles

Interior and Exterior Angels of Triangles

Multiple Choice

Pick any triangle in the picture and add up all of its angles. What does it add up to?

• 180^o

• 360^o

• 90^o

• 75^o

Multiple Choice

Do all of the pictured triangles have the same angle sum? (Do their angles all add up to the same number?)

• Yes

• No

Interior Angle Sum

No matter what, the sum of all three angles of a triangle will add up to 180 degrees.

This fact will be invaluable throughout this assignment.

The previous slide.

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Open Ended

In your own words, explain how to find the missing angle of a triangle.

Multiple Select

Which of the following would be an appropriate equation to solve for the missing angle?

• 180 = 68 + 47 + x

• 68 + 47 + x = 180

• 47 + 68 + x = 90

• 68 + 47 = 180 + x

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The previous slide.

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Multiple Choice

Triangle ABC is an isosceles triangle. What would be an appropriate equation to solve for angle A?

• 180 = 120 + x + x

• 120 = x + x

• 180 = 120 + 120 + x

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The previous slide.

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Multiple Select

Which would be an appropriate equation to solve this triangle?

(Multiple answers are correct.)

• 180 = 4x + 6 + 3x + 14 + 90

• 180 = 4x + 3x + 6 + 14 + 90

• 180 = 7x + 110

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Solving for an angle:

Once you know that x is equal to 7, you can find the value for each missing angle by substituting 7 for x in each expression:

Ex. Plug 7 into 4x + 6.

4(7) + 6

28 + 6

34

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To solve for x:

48 + 11x - 5 + 9x - 3 = 180

Combine like terms

20x + 40 = 180

Subtract 40 from both sides

20x = 140

Divide by 20

x = 7

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To solve for angle A:

Since x = 7, plug 7 into (9x - 3)

9(7) - 3

63 - 3

60

Multiple Select

What do angles A and B equal when added together? (Multiple answers are correct.)

• 75 degrees

• The same as angle C

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To solve for x:

Set up the equation

5x + 7 = 75 + 37

Combine like terms

5x + 7 = 112

Subtract 7 from each side

5x = 105

Divide by 5

x = 21