Splash Screen

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Splash Screen
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Then/Now
You have learned about angles before (previous
course)

• Examine relationships between pairs of angles.

• Examine relationships of angles formed by
  parallel lines and a transversal.

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Vocabulary

• perpendicular lines

Lines that intersect to form right angles

• vertical angles
• adjacent angles
• complementary angles
• supplementary angles
• parallel lines

Two pairs of opposite angles formed by two
intersecting lines. The angles are congruent.
Two angles that have the same vertex, share a
common side, and do not overlap
Two angles whose sum is 90
Two angles whose sum is 180
Two lines in a same plane that do not intersect
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Vocabulary

• transversal

A line that intersects two parallel lines to form
eight angles

• alternate interior angles
• alternate exterior angles
• corresponding angles

Nonadjacent interior angles found on opposite
sides of the transversal. In parallel lines,
these are congruent.
Nonadjacent exterior angles found on opposite
sides of the transversal. In parallel lines,
these are congruent.
Angles that have the same position on two
different parallel lines cut by a transversal.
These angles are congruent.
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Concept A
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Example 1 A
Find a Missing Angle Measure
A. Jun is cutting a tile. Classify the
relationship of ?a and ?b.
Answer The angles are complementary. The sum of
their measures is 90.
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Example 1 B
Find a Missing Angle Measure
B. If m?a 53, what is the measure of ?b?
m?b 53 90 Write the equation. m?b
53 53 90 53 Subtract 53 from each side.
m?b 37 Simplify.
Answer m?b 37
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Example 1 CYP A
A. Elisa is cutting a piece of fabric. What is
the relationship between ?a and ?b?
A. They are complementary. B. They are
supplementary. C. They are congruent. D. They are
obtuse.

1. A
2. B
3. C
4. D

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Example 1 CYP B
B. If m?a 40, what is m?b?
A. 140 B. 220 C. 50 D. 90

1. A
2. B
3. C
4. D

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Concept B
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Example 2 A
Find Measures of Angles Formed by Parallel Lines
A. Classify the relationship between ?9 and ?13.
Answer Since ?9 and ?13 are corresponding
angles, they are congruent.
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Example 2
Find Measures of Angles Formed by Parallel Lines
B. If m?13 is 75, find m?11 and m?15.
Since ?13 and ?11 are alternate interior
angles, they are congruent. So, m?11 75. ?11
and ?15 are corresponding angles and are
congruent. So, m?15 75.
Answer m?11 75 and m?15 75
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Example 2 CYP A
A. What is the relationship between ?1 and ?5?
A. They are corresponding and congruent. B. They
are adjacent and supplementary. C. They are
corresponding and supplementary. D. They are
adjacent and congruent.

1. A
2. B
3. C
4. D

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Example 2 CYP B
B. If m?3 78, what is m?7?
A. 12 B. 22 C. 78 D. 102

1. A
2. B
3. C
4. D

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Example 3
Use Algebra to Find Missing Angle Measures
ALGEBRA Angles DEF and WXY are complementary
angles, with m?DEF 2x and m?WXY 3x 20.
Find the measures of ?DEF and ?WXY.
Step 1 Find the value of x.
m?DEF m?WXY 90 Complementary angles 2x
3x 20 90 Replace m?DEF with 2x and m?WXY
with 3x 20.
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Example 3
Use Algebra to Find Missing Angle Measures
Combine like terms.
Add 20 to each side.
Simplify.
Divide each side by 5.
Simplify.
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Example 3
Use Algebra to Find Missing Angle Measures
Step 2 Replace x with 22 to find the measure of
each angle.
m?DEF 2x m?WXY 3x 20 2(22)
or 44 3(22) 20 or 46
Answer m?DEF 44 and m?WXY 46
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Example 3
Angles RST and ABC are complementary angles with
m?RST 3x and m?ABC x 10. What are the
measures of ?ABC and ?RST?
A. m?ABC 12 and m?RST 78 B. m?ABC 20 and
m?RST 70 C. m?ABC 30 and m?RST
60 D. m?ABC 30 and m?RST 70

1. A
2. B
3. C
4. D

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End of the Lesson