Section 1 4 Measuring Angles Objective Students will

Section 1. 4 Measuring Angles

Objective: • Students will be able to: find and compare measures of angles 1. 4 Measuring Angles

Vocabulary: angle sides of an angle vertex of an angle measure of an angle acute angle right angle obtuse angle straight angle congruent angles 1. 4 Measuring Angles

When you name angles using three points, the vertex MUST go in the middle. 1. 4 Measuring Angles

The interior of an angle is the region containing all of the points between the two sides of the angle. The exterior of an angle is the region containing all of the points outside of the angle. 1. 4 Measuring Angles

Problem 1: What are the two other names for <1? What are the two other names for <KML? Would it be correct to name any of the angles <M? Explain!! 1. 4 Measuring Angles

Problem 1 Solution: What are the two other names for <1? < 1 is also named: < JMK and <KMJ What are the two other names for <KML? < KML is also named: < 2 and < LKM Would it be correct to name any of the angles <M? Explain!! NO. M is shared by more than one angle. 1. 4 Measuring Angles

One way to measure the size of an angle is in degrees. To indicate the measure of an angle, write a lowercase m in front of the angle symbol. In the diagram, the measure of <A is 62. You write this as m<A = 62. 1. 4 Measuring Angles

The Protractor Postulate allows you to find the measure of an angle. 1. 4 Measuring Angles

The measure of <COD is the absolute value of the difference of the real numbers paired with Ray OC and Ray OD. m < COD = | 1350 – 330 | m < COD = | 1020 | m < COD = 1020 1. 4 Measuring Angles

Classifying Angles: ACUTE RIGHT OBTUSE STRAIGHT 1. 4 Measuring Angles

Problem 2: What are the measures of <LKN, JKL, and JKN? Classify each angle as acute, right, obtuse, or straight. 1. 4 Measuring Angles

Problem 2 Solution: m <LKN | 1450 – 350 | | 1100 | m < LKN = 1100 m < JKL m < JKN | 900 – 1450 | | – 550 | m < LKN = 550 | 00 – 900 | | – 900 | m < LKN =900 1. 4 Measuring Angles

Angles with the same measure are congruent angles. This means that: if m<A = m<B, then <A <B. You can mark angles with arcs to show that they are congruent. If there is more than one set of congruent angles, each set is marked with the same number of arcs. 1. 4 Measuring Angles

Problem 3: Synchronized swimmers form angles with their bodies, as show in the photo. If m<GHJ = 90, what is m<KLM? 1. 4 Measuring Angles

Problem 3 Solution: If m<GHJ = 90, what is m<KLM? m < GHJ = m < MLK because they both have two arcs thus m < MLK = 90 1. 4 Measuring Angles

1. 4 Measuring Angles

Problem 4: If m<ROT = 155, what are m<ROS and m<TOPS? 1. 4 Measuring Angles

Problem 4 Solution: Given: m<ROT = 155, We know: m< ROT = m<RSO + m<SOT m< ROT = (4 x – 20) + (3 x + 14) m< ROT = 4 x – 20 + 3 x + 14 m< ROT = 7 x – 6 155 = 7 x – 6 +6 +6 161 = 7 x 23 = x 1. 4 Measuring Angles

Problem 4 Solution: Remember that : 23 = x m<RSO = (4 x -20) and m<SOT = (3 x + 14) m< ROS = (4(23) – 20) and m<SOT = (3(23) + 14) m< ROS = (92 – 20) and m<SOT = (69 + 14) m< ROS = 72 and m<SOT = 83 1. 4 Measuring Angles

Problem 5: <DEF is a straight angle. What are m<DEC and m<CEF? 1. 4 Measuring Angles

Problem 5 Solution: <DEF is a straight angle = 180 We know: m< DEF = m<DEC + m<CEF 180 = (11 x – 12) + (2 x + 10) 180 = 13 x – 2 182 = 13 x 14 = x 1. 4 Measuring Angles

Problem 5 Solution: Remember that : 14 = x m<RSO = (11 x -12) and m<SOT = (2 x + 10) m< ROS = (11(14) – 12) and m<SOT = (2(14) + 10) m< ROS = (154 – 12) and m<SOT = (28 + 10) m< ROS = 142 and m<SOT = 38 Notice : m< ROS = 142 + m<SOT = 38 180 1. 4 Measuring Angles

1. 4 Measuring Angles

1. 4 Measuring Angles