Download Angle 1 + Angle 2 = 180

Chapter 7: GEOMETRY
Section 2
Identifying and
Classifying Angles
California Standards
 Measurement and Geometry 2.0:
 Students identify and describe the properties of 2-
dimensional figures.
 Measurement and Geometry 2.1:
 Identify angles as VERTICAL, ADJACENT,
COMPLEMENTARY, or SUPPLEMENTARY and provide
descriptions of these terms.
 Measurement and Geometry 2.2:
 Use the Properties of Complementary and Supplementary
Angles to solve problems involving an Unknown Angle
Key Vocabulary
 ANGLE: A figure formed by two rays with a shared vertex or common endpoint.
 VERTEX: The point of intersection of two sides of an angle.
 ACUTE ANGLE: An angle that measures between 0° and 90°.
 OBTUSE ANGLE: An angle that measures between 90° and 180°.
 RIGHT ANGLE: An angle that measures EXACTLY 90°.
 STRAIGHT ANGLE: An angle that measures EXACTLY 180°
 COMPLEMENTARY ANGLES: 2 angles that measure 90°.
 SUPPLEMENTARY ANGLES: 2 angles that measure 180°.
 ADJACENT ANGLES: Angles that lay side to side and share a vertex.
 VERTICAL ANGLES: Angles that are formed by intersecting lines and are
OPPOSITE of each other.
 CONGRUENT ANGLES: Angles that EQUAL each other in measure.
What is an ANGLE?
 An ANGLE is a figure formed by two rays with a common
endpoint.
 Angles can be measured with a PROTRACTOR. The measure
of an angle can be any number between 0° and 180°.
 Angles can be labeled with numbers or letters.
 When angles are unknown, numbers can be used.
 When you want to formally call an angle you can identify it by
three letters. Example Angle BCD would be an angle formed
by Ray BC and Ray CD. Point C is the shared endpoint.
CLASSIFYING ANGLES
 Angles can be classified by their MEASURE.
 Protractors are used to find the EXACT angle measure.
 Once the Angle Measure is found, Angles fall into one of the
following categories:
 ACUTE: An angle that measures between 0° and 90°.
 OBTUSE: An angle that measures between 90° and 180°.
 RIGHT: An angle that measures EXACTLY 90°.
 STRAIGHT: An angle that measures EXACTLY 180°
COMPLEMENTARY ANGLES
 When you have 2 angles that measure 90 degrees, they are referred
to as being COMPLEMENTARY.
 Here, 2 small measure or ACUTE angles will combine to equal 90°.
 The BASIC formula to solve COMPLEMENTARY Angles is:
 Angle 1 + Angle 2 = 90°.
 Example:
 Two angles are COMPLEMENTARY, Angle 1 measures 34°.
Please find the measure for the Angle 2.
 Angle 1 + Angle 2 = 90°
-Here, the Basic Formula is used
 34° + Angle 2 = 90°
-Drop in the known Angle Measures
-34°
-34°
-Solve Algebraically
 Angle 2 = 56°
-Result is your answer
Finding MORE Complements
 Two angles are COMPLEMENTARY, Angle 1 measures 28°. Please find the
measure for the Angle 2.
 Angle 1 + Angle 2 = 90°
 28° + Angle 2 = 90°
-28°
-28°
 Angle 2 = 62°
-Basic Formula is used
-Drop in the known Angle Measures
-Solve Algebraically
-Result is your answer
 Two angles are COMPLEMENTARY, Angle 1 measures 35°. Please find the
measure for the Angle 2.
 Angle 1 + Angle 2 = 90°
 35° + Angle 2 = 90°
-35°
-35°
 Angle 2 = 55°
-Basic Formula is used
-Drop in the known Angle Measures
-Solve Algebraically
-Result is your answer
SUPPLEMENTARY ANGLES
 When you have 2 angles that measure 180 degrees(180°), they are
referred to as being SUPPLEMENTARY.
 Here, 2 angles of any measure will combine to equal 180°.
 The BASIC formula to solve COMPLEMENTARY Angles is:
 Angle 1 + Angle 2 = 180°.
 Example:
 Two angles are SUPPLEMENTARY, Angle 1 measures 105°.
Please find the measure for the Angle 2.
 Angle 1 + Angle 2 = 180°
-Here, the Basic Formula is used
 105° + Angle 2 = 180°
-Drop in the known Angle Measures
-105°
-105°
-Solve Algebraically
 Angle 2 = 75°
-Result is your answer
Finding MORE Supplements
 Two angles are SUPPLEMENTARY, Angle 1 measures 85°. Please find the
measure for the Angle 2.
 Angle 1 + Angle 2 = 180°
 85° + Angle 2 = 180°
-85°
-85°
 Angle 2 = 95°
-Basic Formula is used
-Drop in the known Angle Measures
-Solve Algebraically
-Result is your answer
 Two angles are SUPPLEMENTARY, Angle 1 measures 114°. Please find the
measure for the Angle 2.
 Angle 1 + Angle 2 = 180°
 114° + Angle 2 = 180°
-114°
-114°
 Angle 2 = 66°
-Basic Formula is used
-Drop in the known Angle Measures
-Solve Algebraically
-Result is your answer
ADJACENT & VERTICAL ANGLES
 What are ADJACENT Angles?
 What are VERTICAL Angles?
 ADJACENT angles are Angles
 VERTICAL Angles are Angles
that sit right next to each other.
 They share a side and an
endpoint.
 They BUTT up against each
other.
 Think of them like BEST
Friends who have to be near
each other ALL the time.
that are OPPOSITE to each
other.
 They are made from a pair of
Intersecting lines and share a
point.
 Some people think of them as
MIRROR Images of each other.
QUICK REVIEW
 Classifying Angles:
 There are 4 ways an Angle can be classified:
 ACUTE (Under 90°), OBTUSE (Over 90° but Under 180°), RIGHT (EXACTLY 90°),
or STRAIGHT (EXACTLY 180°).
 Finding Complements:
 Angle 1 + Angle 2 = 90°
 Finding Supplements
 Angle 1 + Angle 2 = 180°
 Types of Angles
 Adjacent Angles: Angles that share a vertex & a side but no interior points.
 Vertical Angles: Angles formed by Intersecting Lines and are OPPOSITE from
each other.
 Congruent Angles: Angles that possess the SAME measure.
Check for Understanding
 Please determine the BEST answer for the
following expression.
 Carry out ALL work and calculations in your
NOTES for later reference
 Please write your answer on your wipe boards
and wait for the teacher’s signal.
 On the count of 3, hold up your wipe boards.
C4U Question #1
Question #1:
 Two angles are COMPLEMENTARY, Angle 1
measures 29°. Please find the measure for the
Angle 2.
 Please work out the problem within your notes
 Write the correct answer on your wipe board.
 Wait for Teacher’s Signal.
C4U Question #2
Question #2:
 Two angles are COMPLEMENTARY, Angle 1
measures 61°. Please find the measure for the
Angle 2.
 Please work out the problem within your notes
 Write the correct answer on your wipe board.
 Wait for Teacher’s Signal.
C4U Question #3
Question #3:
 Two angles are SUPPLEMENTARY, Angle 1
measures 41°. Please find the measure for the
Angle 2.
 Please work out the problem within your notes
 Write the correct answer on your wipe board.
 Wait for Teacher’s Signal.
C4U Question #4
Question #4:
 Two angles are SUPPLEMENTARY, Angle 1
measures 73°. Please find the measure for the
Angle 2.
 Please work out the problem within your notes
 Write the correct answer on your wipe board.
 Wait for Teacher’s Signal.
GUIDED PRACTICE
 Students will work on a worksheet/book work, focusing only on the
problems assigned by the teacher.
 Work carefully, show your problem solving process, and double check
all calculations.
 Use scratch paper to carry out your work.
 Once you have completed the assigned problems, please raise your
pencil.
 The teacher will then check your work and release you to complete
the independent practice.
INDEPENDENT PRACTICE
 Once you have been signed off and released to complete
Independent Practice, please complete the following assignment: