Learn to find unknown angles in triangles'

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Learn to find unknown angles in triangles.
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Vocabulary
Triangle Sum Theorem acute triangle right
triangle obtuse triangle equilateral
triangle isosceles triangle scalene triangle
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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 sides of the triangle are transversals to the
parallel lines.
The three angles in the triangle can be arranged
to form a straight line or 180.
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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
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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
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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
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Try This Example 1A
Find a in the acute triangle.
88 38 a 180
38
126 a 180
a 54
88
a
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Try This Example 1B
Find b in the right triangle.
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38 90 b 180
128 b 180
b 52
b
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Try This Example 1C
Find c in the obtuse triangle.
24 38 c 180
38
62 c 180
24
c
c 118
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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 angle measures in the equilateral triangle.
3b 180
Triangle Sum Theorem
Divide both sides by 3.
b 60
All three angles measure 60.
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Additional Example 2B Finding Angles in
Equilateral, Isosceles, and Scalene Triangles
Find angle measures in the isosceles triangle.
62 t t 180
Triangle Sum Theorem
62 2t 180
Combine like terms.
Subtract 62 from both sides.
2t 118
Divide both sides by 2.
t 59
The angles labeled t measure 59.
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Additional Example 2C Finding Angles in
Equilateral, Isosceles, and Scalene Triangles
Find angle measures in the scalene triangle.
2x 3x 5x 180
Triangle Sum Theorem
Combine like terms.
10x 180
Divide both sides by 10.
x 18
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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Try This Example 2A
Find angle measures in the isosceles triangle.
39 t t 180
Triangle Sum Theorem
Combine like terms.
39 2t 180
Subtract 39 from both sides.
2t 141
Divide both sides by 2
39
t 70.5
t
The angles labeled t measure 70.5.
t
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Try This Example 2B
Find angle measures in the scalene triangle.
3x 7x 10x 180
Triangle Sum Theorem
20x 180
Combine like terms.
Divide both sides by 20.
x 9
10x
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.
3x
7x
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Try This Example 2C
Find angle measures in the equilateral triangle.
3x 180
Triangle Sum Theorem
x
x 60
x
x
All three angles measure 60.
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Additional Example 3 Finding Angles in a
Triangle that Meets Given Conditions
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.
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Additional Example 3 Continued
x 6x 3x 180
Triangle Sum Theorem
10x 180
Combine like terms.
Divide both sides by 10.
x 18
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Additional Example 3 Continued
The angles measure 18, 54, and 108. The
triangle is an obtuse scalene triangle.
x 18
3 18 54
6 18 108
X 18
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Try This Example 3
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.
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Try This Example 3 Continued
Triangle Sum Theorem
x 3x x 180
5x 180
Combine like terms.
Divide both sides by 5.
x 36
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Try This Example 3 Continued
The angles measure 36, 36, and 108. The
triangle is an obtuse isosceles triangle.
x 36
3 36 108
x 36
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Lesson Quiz Part 1
1. Find the missing angle measure in the acute
triangle shown.
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2. Find the missing angle measure in the right
triangle shown.
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Lesson Quiz Part 2
3. Find the missing angle measure in an acute
triangle with angle measures of 67 and 63.
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4. Find the missing angle measure in an obtuse
triangle with angle measures of 10 and 15.
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