1. 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?

2. Warm-Up Exercises EXAMPLE 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.

3. 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

4. Example

5. Warm-Up Exercises 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.

6. Warm-Up Exercises EXAMPLE 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. o o o 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. o o o c. m GHJ = 180. It is a straight angle. o d. m GHL= 90. It is a right angle. o

7. Warm-Up Exercises GUIDED 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

8. Warm-Up Exercises GUIDED PRACTICE for Examples 1and 2 2. Draw a pair of opposite rays. What type of angle do the rays form? ANSWER Straight Angle

9. Warm-Up Exercises EXAMPLE 3 Find angle measures o ALGEBRA 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 o o

10. Warm-Up Exercises EXAMPLE 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

11. Warm-Up Exercises GUIDED 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°

12. Warm-Up Exercises GUIDED PRACTICE for Example 3 4. Given that EFG is a right angle, find m EFH and m HFG. ANSWER 60°, 30°

13. Warm-Up Exercises 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? Trapeze SOLUTION There are two pairs of congruent angles: DEF JKL and DEG GKL. ~~ Because  DEG GKL, DEG = m GKL. So, m GKL = 157°. ~

14. Warm-Up Exercises GUIDED 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

15. Warm-Up Exercises 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. o o o Use the diagram shown. m PTS = 121°, m QPT = 84° ANSWER

16. 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. o 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°.

17. Warm-Up Exercises GUIDED 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

18. Warm-Up Exercises Daily 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

19. Warm-Up Exercises Daily Homework Quiz ANSWER 14 o ANSWER 72 o 4. If m DEG = 84, Find m FEG. o 5. if XY bisects ZXW and m XZY = 36, find m ZXW o

20. 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.