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

2. x + 90 + 11 = 180

3. 2x + 18 = 180

4. 180 = 2x + 72 + x

Course 3

7-3 Angles in Triangles

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

Course 3

7-3 Angles in Triangles

Learn to find unknown angles in triangles.

Course 3

7-3 Angles in Triangles

TB P. 336-340

VocabularyTriangle Sum Theorem

acute triangle

right triangle

obtuse triangle

equilateral triangle

isosceles triangle

scalene triangle

Insert Lesson Title Here

Course 3

7-3 Angles in Triangles

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.

Course 3

7-3 Angles in Triangles

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.

Course 3

7-3 Angles in Triangles

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

Course 3

7-3 Angles in Triangles

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°

Course 3

7-3 Angles in Triangles

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°

Course 3

7-3 Angles in Triangles

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°

Course 3

7-3 Angles in Triangles

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.

Course 3

7-3 Angles in Triangles

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.

Course 3

7-3 Angles in Triangles

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

7-3 Angles in Triangles

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.

Triangle Sum Theorem

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°.

Course 3

7-3 Angles in Triangles

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.

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

Course 3

7-3 Angles in Triangles

Additional Example 3 Continued

x° + 6x° + 3x° = 180°

10x° = 180° 10 10

x° = 18°

Triangle Sum Theorem

Combine like terms.Divide both sides by 10.

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

12

Course 3

7-3 Angles in Triangles

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

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

12

Course 3

7-3 Angles in Triangles

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°

Course 3

7-3 Angles in Triangles

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

7-3 Angles in Triangles