Learn to identify angles and angle pairs.
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Transcript of Learn to identify angles and angle pairs.
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Learn to identify angles and angle pairs.
Course 2
8-2 Classifying Angles
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Vocabularyanglevertexright angleacute angleobtuse anglestraight angleadjacent anglescomplementary anglessupplementary anglesvertical angles
Insert Lesson Title Here
Course 2
8-2 Classifying Angles
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An angle is formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is the vertex.
Angles are measured in degrees (°).
A
CB1
Vertex
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An angle’s measure determines the type of angle it is.A right angle is an angle that that measures exactly 90°. Thesymbol indicates a right angle.An acute angle is an anglethat measures less than 90°.An obtuse angle is an anglethat measures more than 90°but less than180°.A straight angle is an anglethat measures 180°.
Course 2
8-2 Classifying Angles
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Tell whether each angle is acute, right, obtuse or straight.
Additional Example 1: Classifying Angles
A. B.
obtuse angle acute angle
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8-2 Classifying Angles
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Course 2
8-2 Classifying Angles
You can name this angle ABC, CBA, B, or 1.
Reading MathA •
B • • C
1
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Check It Out: Example 1
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Tell whether each angle is acute, right, obtuse, or straight.
A. B.
straight angle acute angle
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8-2 Classifying Angles
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Two angles having a common side and common vertex and lying on opposite sides of their common side, then angles are adjacent to each other.
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If the sum of the measures of two angles is90°, then the angles are complementary angles. If the sum of the measures of twoangles is 180°, then the angles are supplementary angles.
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Vertical angles are opposite angles. Two intersecting liens form two pairs of vertical angles and they are congruent.
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Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Additional Example 2A: Identifying Complementary and Supplementary Angles
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8-2 Classifying Angles
OMP and PMQ
Since 60° + 30° = 90°, PMQ and OMP are complementary. O
N
P Q
RM
To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mOMP = 60°.
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Course 2
8-2 Classifying Angles
If the angle you are measuring appears obtuse, then it measure is greater than 90°. If the angle is acute, its measure is less than 90°.
Reading Math
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Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Additional Example 2B: Identifying Complementary and Supplementary Angles
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NMO and OMRmNMO = 15° and mOMR = 165°
O
N
P Q
RM
Since 15° + 165° = 180°, NMO and OMR are supplementary.
Read mNMO as “the measure of angle NMO.”
Reading Math
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Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Additional Example 2C: Identifying Complementary and Supplementary Angles
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PMQ and QMR
O
N
P Q
RM
Since 30° + 75° = 105°, PMQ and QMR are neither complementary or supplementary.
To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mQMR = 75°.
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Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Check It Out: Example 2A
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BAC and CAFmBAC = 35° and mCAF = 145°
C
B
D
E
FA
Since 35° + 145° = 180°, BAC and CAF are supplementary.
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Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Check It Out: Example 2B
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8-2 Classifying Angles
CAD and EAF
Since 55° + 35° = 90°, CAD and EAF are complementary.
C
B
D
E
FA
To find mCAD start with the measure that DA crosses, 90°, and subtract the measure that CA crosses, 35°. mCAD = 90° - 35° = 55°. mEAF = 35°.
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Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Check It Out: Example 2C
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BAC and EAFmBAC = 35° and mEAF = 35°
C
B
D
E
FA
Since 35° + 35° = 70°, BAC and EAF are neither supplementary or complementary.
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Angles A and B are complementary. If mA is 56°, what is the mB?
Additional Example 3: Finding Angle Measures
Since A and B are complementary, mA + mB = 90°.
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mA + mB = 90° 56° + mB = 90°
– 56° – 56°
mB = 34°
Substitute 56° for mA.Subtract 56° from both sides to isolate mB.
The measure of B = 34°.
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Angles P and Q are supplementary. If mP is 32°, what is the mQ?
Check It Out: Example 3
Since P and Q are complementary, mP + mQ = 180°.
Course 2
8-2 Classifying Angles
mP + mQ = 180° 32° + mQ = 180°
– 32° – 32°
mQ = 148°
Substitute 32° for mP.Subtract 32° from both sides to isolate mQ.
The measure of Q = 148°.