Learn to identify angles and angle pairs.

Course 2

8-2 Classifying Angles

Vocabularyanglevertexright angleacute angleobtuse anglestraight angleadjacent anglescomplementary anglessupplementary anglesvertical angles

Insert Lesson Title Here

Course 2

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

Course 2

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°. 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

Tell whether each angle is acute, right, obtuse or straight.

Additional Example 1: Classifying Angles

A. B.

obtuse angle acute angle

Course 2

8-2 Classifying Angles

Course 2

8-2 Classifying Angles

You can name this angle ABC, CBA, B, or 1.

Reading MathA •

B • • C

1

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

Course 2

8-2 Classifying Angles

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.

Course 2

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.

Course 2

8-2 Classifying Angles

Vertical angles are opposite angles. Two intersecting liens form two pairs of vertical angles and they are congruent.

Course 2

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

Course 2

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°.

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

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Additional Example 2B: Identifying Complementary and Supplementary Angles

Course 2

8-2 Classifying 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

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Additional Example 2C: Identifying Complementary and Supplementary Angles

Course 2

8-2 Classifying Angles

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°.

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Check It Out: Example 2A

Course 2

8-2 Classifying Angles

BAC and CAFmBAC = 35° and mCAF = 145°

C

B

D

E

FA

Since 35° + 145° = 180°, BAC and CAF are supplementary.

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Check It Out: Example 2B

Course 2

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°.

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Check It Out: Example 2C

Course 2

8-2 Classifying Angles

BAC and EAFmBAC = 35° and mEAF = 35°

C

B

D

E

FA

Since 35° + 35° = 70°, BAC and EAF are neither supplementary or complementary.

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°.

Course 2

8-2 Classifying Angles

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°.

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°.