1.4: Angle Measure

1. 1.4: Angle Measure • SOL: G4 • Objectives: • Measure and classify angles. • Identify special angle pairs. • Use the special angle pairs to find angle measures.

2. B Noncollinear rays A A C Common Endpoint Angle • formed by two noncollinear rays that have a common endpoint.

3. Side AB B A A Vertex A C Side AC Sides of an Angle • The rays that make the angle Vertex of an Angle • The common endpoint

4. B A 4 C Note the vertex is the middle point listed Symbols • When we name an angle, the vertex point is always in the middle • The following are the different ways we can name this angle: A, BAC, CAB, 4

5. Any point inside the angle Exterior Exterior Interior of an Angle Exterior of an Angle • Any point outside the angle Interior

6. BG and BE or BF Example 1: Use the diagram to answer a, b, and c. a.) Name all angles that have B as a vertex. b.) Name the sides of 5. c.) Write another name for 6. ∡ABG, ∡ABD, ∡DBE or ∡DBF, ∡EBG or ∡FBG, ∡5, ∡6, ∡7 ∡DBE or ∡DBF

7. Measuring Angles The protractor has two scales running from 0 to 180 degrees in opposite directions. These are the scales we use to determine the measure of the angle Place the center point of the protractor on the vertex Align the 0 on either side of the scale with one side of the angle. (Paying attention to which direction the angle is opening To measure an angle, you use a protractor.

8. Example 2: Since QP is aligned with the 0 on the outer scale, use the outer scale to find that QR intersects the scale at 65 degrees. Find the measure of PQR. R 65° Q P

9. Measures 90 Written as mA = 90 A This symbol means, right angle, perpendicular B Classify Angles by Angle Measure Right Angle Acute Angle • Measures less than 90 • Written as mB < 90

10. A B C C Classify Angles by Angle Measure Obtuse Angle Straight Angle (Line) • Measures greater than 90 • Measures 180 • Written as mC > 90

11. Example 3: Measure the angle and classify it. 12°, Acute

12. Example 4: Measure the angle and classify it. 99°, Acute

13. Example 5: Measure the angle and classify it. 69°, Acute

14. Congruent Angles • Angles that have the same measure • Symbols: NMPQMR

15. Postulate 1.8: Angle Addition Postulate • If point B is in the interior of ∠AOC , then m∠AOB + m∠BOC = m∠AOC

16. Example 6: M If m∠EFG = 23°, what is the m∠EFH? D 12° Apply the angle addition postulate. A m∡EFG - m∡GFH = m∡EFH 23° K 23° - 11° = 12° C 68° L 46° H J B E If m∠KJL = 117°, what is the m∠KJM? What is the m∡ABC? 11° G 69° 49° m∡ABD + m∡CBD = m∡ABC m∡KJL - m∡LJM = m∡KJM 23° + 46° = 69° F 117° - 68° = 49°

17. Example 7: If m∠RQT = 155°, what are the m∠RQS and m∠SQT? m∡RQS + m∡TQS = m∡RQT Check: 72° + 83° = 155° (4x – 20) + (3x + 14) = 155° 7x – 6= 155° + 6 + 6 7x = 161° 7x = 161° 7 7 x = 23° m∡RQS = 4x – 20 = 4(23) – 20 = 72° m∡TQS = 3x + 14 = 3(23) + 14 = 83°

18. Example 8: ∠DEF is a straight angle. What are the m∠DEC and m∠CEF? m∡DEC + m∡FEC = m∡DEF (11x – 12) + (2x + 10) = 180° 13x – 2 = 180° + 2 + 2 13x = 182° Check: 142° + 38° = 180° 13x = 182° 13 13 x = 14° m∡DEC = 11x – 12 = 11(14) – 12 = 142° m∡FEC = 2x + 10 = 2(14) + 10 = 38°