Section 1.4 Measuring Angles 1.4 Measuring Angles

Objective: Students will be able to: find and compare measures of angles 1.4 Measuring Angles

Vocabulary: angleright angle sides of an angleobtuse angle vertex of an anglestraight angle measure of an anglecongruent angles acute angle 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? What are the two other names for <KML? Would it be correct to name any of the angles <M? Explain!! 1.4 Measuring Angles < 1 is also named: < JMK and <KMJ < KML is also named: < 2 and < LKM NO. M is shared by more than one angle.

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 = 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. 1.4 Measuring Angles m < COD = | – 33 0 | m < COD = | | m < COD = 102 0

Classifying Angles: ACUTE RIGHT OBTUSESTRAIGHT 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 <LKNm < JKL m < JKN 1.4 Measuring Angles | – 35 0 | | | m < LKN = | 90 0 – | | – 55 0 | m < LKN = 55 0 | 0 0 – 90 0 | | – 90 0 | m < LKN =90 0

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? 1.4 Measuring Angles m < GHJ = m < MLK because they both have two arcs thus m < MLK = 90

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, 1.4 Measuring Angles We know: m< ROT = m<RSO + m<SOT m< ROT = (4x – 20) + (3x + 14) m< ROT = 4x – x + 14 m< ROT = 7x – = 7x – = 7x 23 = x

Problem 4 Solution: 1.4 Measuring Angles m< ROS = (4(23) – 20) and m<SOT = (3(23) + 14) Remember that : 23 = x m< ROS = (92 – 20) and m<SOT = ( ) m< ROS = 72 and m<SOT = 83 m<RSO = (4x -20) and m<SOT = (3x + 14)

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 = Measuring Angles We know: m< DEF = m<DEC + m<CEF 180 = (11x – 12) + (2x + 10) 180 = 13x – = 13x 14 = x

Problem 5 Solution: 1.4 Measuring Angles m< ROS = (11(14) – 12) and m<SOT = (2(14) + 10) Remember that : 14 = x m< ROS = (154 – 12) and m<SOT = ( ) m< ROS = 142 and m<SOT = 38 m<RSO = (11x -12) and m<SOT = (2x + 10) Notice : m< ROS = m<SOT = 38  180

1.4 Measuring Angles