1.4 Measure and Classify Angles

You will name, measure and classify angles.

Classifying Angles• Acute angle: between 0 and 90

• Right angle: exactly 90 degrees• Symbol:

• Obtuse Angle: between 90 and 180

• Straight angle: exactly 180 degrees

Angles

• Naming Angles– Use 3 capital letters – Vertex in the middle– Can use one capital letter if it is the vertex and it is

obvious which angle you are referring to– Can use the number located inside the angle

• Angle Bisector– Divides the angle into 2 congruent parts

Naming angles

• Name this angle three different ways

Naming angles

• Name this angle three different ways

Naming angles

• Name this angle four different ways

Name this angle in 4 ways

Congruent Angles

• Have the same angle measure

Congruent Angles

• Can be marked using the same number of hash marks.

H

W

F

Q

Angle Addition Postulate

• Smaller angles can be added together to form larger angles if they share a common vertex.

Given that the m<LKN=145⁰, find the m<LKM and m<MKN

GUIDED PRACTICE for Example 3

Find the indicated angle measures.

3. Given that <KLM is a straight angle, find x and m< NLM.

GUIDED PRACTICE for Example 3

4. Given that < EFG is a right angle, find x and m< HFG.

Homework

• Page 28 # 4 – 40 even

• Honors: also # 42, 44, 48, 49, 50

EXAMPLE 2 Measure and classify angles

Use the diagram to find the measure of the indicated angle. Then classify the angle.

a. KHJ b. GHK c. GHJ d. GHL

SOLUTION

A protractor has an inner and an outer scale. When you measure an angle, check to see which scale to use.

Angle Addition Postulate

• When two angles share a ray, a Part+ Part = Whole or Little + Little = Big

• Very similar to segment addition Postulate

Congruent Angles

• Angles that have the same measure• Angle measures are equal: m<A=m<B– The measure of angle A is equal to the measure of

angle B• Angle measures are congruent: <A <B– Angle A is congruent to angle B

• When talking about measures, use equal sign. When talking about congruency, use congruent sign

EXAMPLE 4 Identify congruent angles

The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If m<DEG = 157° ,what is m<GKL?

GUIDED PRACTICE for Example 4

5. Identify all pairs of congruent angles in the diagram.

Use the diagram shown.

GUIDED PRACTICE for Example 4

6. In the diagram, m < PQR = 130 , m<QRS = 84, and m<TSR = 121 . Find the other angle measures in the diagram.

Use the diagram shown.

Angle

• Formed by two rays that meet at an endpoint• Rays are considered sides of an angle• What is the vertex? What rays form the angle?

Vertex of an Angle

• Where the sides of an angle meet.• When naming an angle, vertex goes in the

middleName the three angles in the diagram.

Angle bisector

A ray that divides an angle into two angles that are congruent (equal)

In the diagram at the right, YW bisects < XYZ, and m< XYW = 18. Find m< XYZ.

Protractor Postulate

• The rays of an angle can be matched one to one with real numbers from 0 to 180

• The measure of an angle is equal to the absolute value of the difference between the real number of the rays (much like the segment addition postulate)