Angle Measure ANGLE WHO?

Standard/Objectives: Performance Standard: Solve problems involving complementary, supplementary and congruent angles. Objectives: Use angle postulates Use angle postulates Classify angles as acute, right, obtuse, or straight. Classify angles as acute, right, obtuse, or straight.

Vocabulary: RAY: part of a line that has an endpoint and extends indefinitely in one direction. OPPOSITE RAYS: Two rays going in opposite directions, making a straight line.

ANGLE: Is formed by two noncollinear rays that have a common end point. The rays are called sides. The common endpoint is called a Vertex.

Symbol for a AB AB BC BC C B A B RAY

SYMBOL FOR ANGLES: Naming the angles: 1. < ABC 2. < CBA 3. < B Naming the sides: 1. A B 2. B C A B C D E D= Exterior point E= Interior point E D= Exterior point E= Interior point E

Example: Name all angles: Name all sides: ANSWERS 1. < RPQ 2. < QPS 3. < RPS 4. < 1 5. < 2 ANSWERS RP PQ PS R P S Q 21 I SO GOT THIS!

CLASSIFING ANGLES: ANGLES RIGHT ANGLE m<A=90 ACUTE ANGLE m<A <90 OBTUSE ANGLE m 90

Classifying Angles Angles are classified as acute, right, obtuse, and straight, according to their measures. Angles have measures greater than 0° and less than or equal to 180°. Angles are classified as acute, right, obtuse, and straight, according to their measures. Angles have measures greater than 0° and less than or equal to 180°.

EXAMPLE OF EACH ANGLE: find the following: Right angle m< QAR Acute angle m< 1 Obtuse angle m< PTW A R Q 1 P T W

Note: The measure of  A is denoted by m  A. The measure of an angle can be approximated using a protractor, using units called degrees(°). For instance,  BAC has a measure of 50°, which can be written as The measure of  A is denoted by m  A. The measure of an angle can be approximated using a protractor, using units called degrees(°). For instance,  BAC has a measure of 50°, which can be written as m  BAC = 50°. B A C

more... Angles that have the same measure are called congruent angles. For instance,  BAC and  DEF each have a measure of 50 °, so they are congruent. Angles that have the same measure are called congruent angles. For instance,  BAC and  DEF each have a measure of 50 °, so they are congruent. 50 °

Note – Geometry doesn’t use equal signs like Algebra MEASURES ARE EQUAL m  BAC = m  DEF ANGLES ARE CONGRUENT  BAC   DEF “is equal to” “is congruent to” Note that there is an m in front when you say equal to; whereas the congruency symbol  ; you would say congruent to. (no m’s in front of the angle symbols).

Congruent angles: Angles that have the same measure. m<NMP m<QMR m<NMP =25 AND m<QMR = 5X Q R P N M 5 X= 255X

Lets do one! <PMN= 7X <QMR=X +24 Find X Find < QMR Q R P N M X+24 7X 7X = X+24 6X = 24 -X-X 66 X = 4 X <QMR= <QMR= <PMN=7X 7(4) 28 <PMN= 28 28

Angle Bisector A ray that divides an angle into two congruent angles. If <A = 2X+3 and <B = 73, find X 2X + 3 = X = <A = <B X= 35

Homework example Steps to solve equations Step 1:simplify each side of the equation. (pemdas) Step 2: move variable to same side. Step 3: get variable by itself. ( do opposite) usually add of subtract. Step 4. multiply or divide. (do opposite) 6X + 5 = 7X – 2 -7X -7X -1X + 5 = X = = X= In the figure, QP and QR are opposite rays and QT bisects <RQS. m<SQT= 7X – 2, find m< RQT PG 33 # ## #9 if m<RQT = 6X+5 and P Q R T S QT bisects <RQS. 7 You can do it!

Postulate 4: Angle Addition Postulate If P is in the interior of  RST, then If P is in the interior of  RST, then m  RSP + m  PST = m  RST

Ex. 2: Calculating Angle Measures VISION. Each eye of a horse wearing blinkers has an angle of vision that measures 100°. The angle of vision that is seen by both eyes measures 60°. VISION. Each eye of a horse wearing blinkers has an angle of vision that measures 100°. The angle of vision that is seen by both eyes measures 60°. Find the angle of vision seen by the left eye alone. Find the angle of vision seen by the left eye alone.

Solution: You can use the Angle Addition Postulate.

Closure Question: Describe how angles are classified. Angles are classified according to their measure. Those measuring less than 90° are acute. Those measuring 90° are right. Those measuring between 90° and 180° are obtuse, and those measuring exactly 180° are straight angles.