1. Insert Lesson Title Here
Vocabulary
angle
vertex
right angle
acute angle
obtuse angle
straight angle
complementary angles
supplementary angles

2. Angles are measured in degrees (°).C B 1
Vertex
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 (°).

3. You can name this angle ABC, CBA, B, or 1. Reading Math

4. 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 than180°.
A straight angle is an angle
that measures 180°.

5. If the sum of the measures of two angles is
90°, then the angles are complementary
angles.
If the sum of the measures of two
angles is 180°, then the angles are
supplementary angles.

6. Adjacent angles have a common vertex and a common side, but no common interior points. Angles 2 and 3 in the diagram are adjacent. Adjacent angles formed by two intersecting lines are supplementary

7. The sum of the measures of the angles in a triangle is 180°.
Angles of a Triangle
The sum of the measures of the angles in a triangle is 180°.
m1 + m2 + m3 = 180° 2 1 3

8. Additional Example 1: Finding an Angle Measure of in a Triangle
55°
Find the measure of the unknown angle.
80° x
The sum of the measures of the angles is 180°.
80° + 55° + x = 180°
135° + x = 180°
Combine like terms.
–135°
–135°
Subtract 135° from both sides.
x = 45°
The measure of the unknown angle is 45°.

9. Check It Out: Example 1
30°
Find the measure of the unknown angle.
90° x
The sum of the measures of the angles is 180°.
90° + 30° + x = 180°
120° + x = 180°
Combine like terms.
–120°
–120°
Subtract 120° from both sides.
x = 60°
The measure of the unknown angle is 60°.

10. Additional Example 1: Classifying Angles
Tell whether each angle is acute, right, obtuse or straight. A. B.
obtuse angle
acute angle

11. Insert Lesson Title Here
Check It Out: Example 1
Tell whether each angle is acute, right, obtuse, or straight. B. A.
straight angle
acute angle

12. Additional Example 2A: Identifying Complementary and Supplementary Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
OMP and PMQ
To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mOMP = 60°. O N P Q R M
Since 60° + 30° = 90°, PMQ and OMP are complementary.

13. 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

14. Additional Example 2B: Identifying Complementary and Supplementary Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
NMO and OMR
mNMO = 15° and mOMR = 165°
Since 15° + 165° = 180°, NMO and OMR are supplementary. O N P Q R M
Read mNMO as “the measure of angle NMO.”
Reading Math

15. Additional Example 2C: Identifying Complementary and Supplementary Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
PMQ and QMR
To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mQMR = 75°. O N P Q R M
Since 30° + 75° = 105°, PMQ and QMR are neither complementary or supplementary.