7-3 Angles in Triangles Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

7-3 Angles in Triangles

Course 3

Warm Up

Problem of the Day

Lesson Presentation

Warm UpSolve each equation.1. 62 + x + 37 = 180

2. x + 90 + 11 = 180

3. 2x + 18 = 180

4. 180 = 2x + 72 + x

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x = 81

x = 79

x = 81

x = 36

Problem of the Day

What is the one hundred fiftieth day of a non-leap year?

May 30

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Learn to find unknown angles in triangles.

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VocabularyTriangle Sum Theorem

acute triangle

right triangle

obtuse triangle

equilateral triangle

isosceles triangle

scalene triangle

Insert Lesson Title Here

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If you tear off two corners of a triangle and place them next to the third corner, the three angles seem to form a straight line.

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Draw a triangle and extend one side. Then draw a line parallel to the extended side, as shown.

The three angles in the triangle can be arranged to form a straight line or 180°.

The sides of the triangle are transversals to the parallel lines.

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An acute triangle has 3 acute angles. A right triangle has 1 right angle. An obtuse triangle has 1 obtuse angle.

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Additional Example 1A: Finding Angles in Acute, Right and Obtuse Triangles

Find p° in the acute triangle.

73° + 44° + p° = 180°

117° + p° = 180°

p° = 63°

–117° –117°

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Additional Example 1B: Finding Angles in Acute, Right, and Obtuse Triangles

Find c° in the right triangle.

42° + 90° + c° = 180°

132° + c° = 180°

c° = 48°

–132° –132°

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Additional Example 1C: Finding Angles in Acute, Right, and Obtuse Triangles

Find m° in the obtuse triangle.

23° + 62° + m° = 180°

85° + m° = 180°

m° = 95°

–85° –85°

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Check It Out: Example 1A

Find a° in the acute triangle.

88° + 38° + a° = 180°

126° + a° = 180°

a° = 54°

–126° –126°

88°

38°

a°

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Find b in the right triangle.

38° + 90° + b° = 180°

128° + b° = 180°

b° = 52°

–128° –128°

38°

b°

Check It Out: Example 1B

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Find c° in the obtuse triangle.

24° + 38° + c° = 180°

62° + c° = 180°

c° = 118°

–62° –62° c°24°

38°

Check It Out: Example 1C

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An equilateral triangle has 3 congruent sides and 3 congruent angles. An isosceles triangle has at least 2 congruent sides and 2 congruent angles. A scalene triangle has no congruent sides and no congruent angles.

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Additional Example 2A: Finding Angles in Equilateral, Isosceles, and Scalene Triangles

Find the angle measures in the equilateral triangle.

3b° = 180°

b° = 60°

3b° 180°3 3

=

Triangle Sum Theorem

All three angles measure 60°.

Divide both sides by 3.

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Additional Example 2B: Finding Angles in Equilateral, Isosceles, and Scalene Triangles

62° + t° + t° = 180°62° + 2t° = 180°

2t° = 118°

–62° –62°

Find the angle measures in the isosceles triangle.

2t° = 118°2 2

t° = 59°

Triangle Sum TheoremCombine like terms.Subtract 62° from both sides.

Divide both sides by 2.

The angles labeled t° measure 59°.Course 3


Additional Example 2C: Finding Angles in Equilateral, Isosceles, and Scalene Triangles

2x° + 3x° + 5x° = 180°

10x° = 180°

x = 18°

10 10

Find the angle measures in the scalene triangle.


Combine like terms.Divide both sides by 10.

The angle labeled 2x° measures 2(18°) = 36°, the angle labeled 3x° measures 3(18°) = 54°, and the angle labeled 5x° measures 5(18°) = 90°.

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Check It Out: Example 2A

39° + t° + t° = 180°39° + 2t° = 180°

2t° = 141°

–39° –39°

Find the angle measures in the isosceles triangle.

2t° = 141°2 2

t° = 70.5°

Triangle Sum TheoremCombine like terms.Subtract 39° from both sides.

Divide both sides by 2

t°t°

39°

The angles labeled t° measure 70.5°.

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3x° + 7x° + 10x° = 180°

20x° = 180°

x = 9°

20 20

Find the angle measures in the scalene triangle.



3x° 7x°

10x°

Check It Out: Example 2B

The angle labeled 3x° measures 3(9°) = 27°, the angle labeled 7x° measures 7(9°) = 63°, and the angle labeled 10x° measures 10(9°) = 90°.

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Find the angle measures in the equilateral triangle.

3x° = 180°

x° = 60°

3x° 180°3 3

=


All three angles measure 60°.

Check It Out: Example 2C

x° x°

x°

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The second angle in a triangle is six times as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible picture.

Let x° = the first angle measure. Then 6x° =

second angle measure, and (6x°) = 3x° =

third angle measure.

12

Additional Example 3: Finding Angles in a Triangle that Meets Given Conditions

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Additional Example 3 Continued

x° + 6x° + 3x° = 180°

10x° = 180° 10 10

x° = 18°



Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle.

12

Course 3


X° = 18°

x° = 18°

6 • 18° = 108°3 • 18° = 54°

The angles measure 18°, 54°, and 108°. The triangle is an obtuse scalene triangle.

Additional Example 3 Continued


12

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The second angle in a triangle is three times larger than the first. The third angle is one third as large as the second. Find the angle measures and draw a possible picture.

Check It Out: Example 3

Let x° = the first angle measure. Then 3x° =

second angle measure, and (3x°) = x° =

third angle measures.

13

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x° + 3x° + x° = 180°

5x° = 180° 5 5

x° = 36°



Check It Out: Example 3 Continued


13

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x° = 36°

x° = 36°3 • 36° = 108°

The angles measure 36°, 36°, and 108°. The triangle is an obtuse isosceles triangle.

36° 36°

108°

Check It Out: Example 3 Continued

Let x° = the first angle measure. Then 3x° = second angle measure, and (3x°) = x° = third angle.

13

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Lesson Quiz: Part I

1. Find the missing angle measure in the acute triangle shown.

2. Find the missing angle measure in the right triangle shown.

38°

55°

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Lesson Quiz: Part II

3. Find the missing angle measure in an acute triangle with angle measures of 67° and 63°.

4. Find the missing angle measure in an obtuse triangle with angle measures of 10° and 15°.

50°

155°

Course 3


Documents

7-3 Angles in Triangles Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation