1.4 Measure and Classify Angles

You will name, measure and classify angles.

Essential Question: How do you identify whether an angle is acute, right, obtuse, or straight?

Warm-Up ExercisesEXAMPLE 1 Name angles

Name the three angles in the diagram.

WXY, or YXW

YXZ, or ZXY

WXZ, or ZXW

You should not name any of these angles X because all three angles have X as their vertex.

Protractor

Step 1: Place the center mark of the protractor on the vertex.

Step 2: Line up the 0-mark with one side of the angle.

Step 3: Read the measure on the protractor scale.

Step 4: Be sure to read the scale that has the 0-mark you are using!

http://youtu.be/fVkgdj-KJUw

Example

Warm-Up ExercisesEXAMPLE 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.

Warm-Up ExercisesEXAMPLE 2 Measure and classify angles

a. HJ is lined up with the 0 on the inner scale of the protractor. HK passes through 55 on the inner scale. So, m KHJ = 55 . It is an acute angle.

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b. HG is lined up with the 0 on the outer scale and HK passes through 125 on the outer scale. So, m GHK = 125 . It is an obtuse angle.

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c. m GHJ = 180. It is a straight angle.

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d. m GHL= 90. It is a right angle.

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Warm-Up ExercisesGUIDED PRACTICE for Examples 1and 2

1. Name all the angles in the diagram. Which angle is a right angle?

PQR , PQS, RQS ; PQS is a right angle .

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 1and 2

2. Draw a pair of opposite rays. What type of angle do the rays form?

ANSWER

Straight Angle

Warm-Up ExercisesEXAMPLE 3 Find angle measures

oALGEBRA Given that m LKN =145 , find m LKM and m MKN.

SOLUTION

STEP 1

Write and solve an equation to find the value of x.

m LKN = m LKM + m MKN Angle Addition Postulate

Substitute angle measures.

145 = 6x + 7 Combine like terms.

Subtract 7 from each side.138 = 6x

Divide each side by 6.23 = x

145 = (2x + 10) + (4x – 3)o oo

Warm-Up ExercisesEXAMPLE 3 Find angle measures

STEP 2

Evaluate the given expressions when x = 23.

m LKM = (2x + 10)° = (2 23 + 10)° = 56°

m MKN = (4x – 3)° = (4 23 – 3)° = 89°

So, m LKM = 56° and m MKN = 89°.ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Example 3

Find the indicated angle measures.

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

ANSWER 125°, 55°

Warm-Up ExercisesGUIDED PRACTICE for Example 3

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

ANSWER 60°, 30°

Warm-Up ExercisesEXAMPLE 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?

Trapeze

SOLUTION There are two pairs of congruent angles:

DEF JKL and DEG GKL.~ ~

Because ∠ DEG GKL, DEG = m GKL. So, m GKL = 157°.

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Warm-Up ExercisesGUIDED PRACTICE for Example 4

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

Use the diagram shown.

T and S, P and R.ANSWER

Warm-Up ExercisesGUIDED 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.

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Use the diagram shown.

m PTS = 121°, m QPT = 84°ANSWER

Warm-Up Exercises

SOLUTION

EXAMPLE 5 Double an angle measure

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

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By the Angle Addition Postulate, m XYZ = m XYW + m WYZ. Because YW bisects XYZ you know that XYW WYZ. ~

So, m XYW = m WYZ, and you can write

m XYZ = m XYW + m WYZ = 18° + 18° = 36°.

Warm-Up ExercisesGUIDED PRACTICE for Example 5

7. Angle MNP is a straight angle, and NQ bisects MNP. Draw MNP And NQ . Use arcs to mark

the congruent angles in your diagram, and give the angle measures of these congruent angles.

90°ANSWER

Warm-Up ExercisesDaily Homework Quiz

1. m A = 90 o

ANSWER right

ANSWER acute

ANSWER obtuse

Classify each angle as acute, obtuse , right and straight.

3. m C = 119 o

2. m B = 62 o

Warm-Up ExercisesDaily Homework Quiz

ANSWER 14o

ANSWER 72o

4. If m DEG = 84 , Find m FEG.o

5. if XY bisects ZXW and m XZY = 36 , find m ZXWo

You will name, measure and classify angles.

Essential Question: How do you identify whether an angle is acute, right, obtuse, or straight?• An angle is formed

by 2 rays that have the same endpoint.

• Angles are classified as acute, right, obtuse, or straight.

• An angle bisector divides an angle into two congruent angles

Acute angles have measure between 0 and 90 degrees, right angles have a measure of 90 degrees, obtuse angles have measures between 90 and 180 degrees, and straight angles have measure 180 degrees.