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8-2 Classifying Angles An angle’s measure determines the type of angle it is. A right angle is an angle that that measures exactly 90°. The symbol indicates a right angle. An acute angle is an angle that measures less than 90°. An obtuse angle is an angle that measures more than 90° but less than 180°. A straight angle is an angle that measures exactly 180°.
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8-2 Classifying Angles
Learn to identify angles and angle pairs.
8-2 Classifying Angles
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
8-2 Classifying AnglesAn 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 than 180°.A straight angle is an anglethat measures exactly 180°.
8-2 Classifying Angles
Tell whether each angle is acute, right, obtuse or straight.
Additional Example 1: Classifying Angles
A. B.
obtuse angle acute angle
8-2 Classifying Angles
You can name this angle ABC, CBA, B, or 1.
Reading MathA •
B • • C
1
8-2 Classifying AnglesCheck It Out: Example 1
Tell whether each angle is acute, right, obtuse, or straight.
A. B.
straight angle acute angle
8-2 Classifying Angles
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.
8-2 Classifying Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Additional Example 2A: Identifying Complementary and Supplementary 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°.
8-2 Classifying Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Additional Example 2B: Identifying Complementary and Supplementary Angles
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
8-2 Classifying Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Additional Example 2C: Identifying Complementary and Supplementary Angles
8-2
PMQ and QMR
O
N
P Q
RM
Since 30° + 75° = 105°, PMQ and QMR are neither complementary nor 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°.
8-2 Classifying Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Check It Out: Example 2A
BAC and CAFmBAC = 35° and mCAF = 145°
C
B
D
E
FA
Since 35° + 145° = 180°, BAC and CAF are supplementary.
8-2 Classifying Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Check It Out: Example 2B
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°.
8-2 Classifying Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
Check It Out: Example 2C
BAC and EAFmBAC = 35° and mEAF = 35°
C
B
D
E
FA
Since 35° + 35° = 70°, BAC and EAF are neither supplementary nor complementary.
8-2 Classifying Angles
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°. mA + mB = 90°
56° + mB = 90° – 56° – 56°
mB = 34°
Substitute 56° for mA.Subtract 56° from both sides.
The measure of B = 34°.
8-2 Classifying Angles
Angles P and Q are supplementary. If mP is 32°, what is the mQ?
Check It Out: Example 3
Since P and Q are supplementary, mP + mQ = 180°. mP + mQ = 180°
32° + mQ = 180° – 32° – 32°
mQ = 148°
Substitute 32° for mP.Subtract 32° from both sides..
The measure of Q = 148°.
8-2 Classifying AnglesLesson Quiz: Part I
Tell whether each angle is acute, right, obtuse, or straight.
1. straight
obtuse2.
8-2 Classifying AnglesLesson Quiz: Part IIUse the diagram to tell whether the angles
are complementary, supplementary, or neither.
3. AZB and BZC neither4. BZC and CZD complementary5. Angles M and N are supplementary. If
mM is 117°, what is mN? 63°
