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Name the angle below in four ways.

Explore methods of naming angles and using a protractor to measure them. Learn about acute, right, obtuse, and straight angles through clear examples and explanations. Enhance your understanding of angle properties.

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Name the angle below in four ways.

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  1. The name can be the number between the sides of the angle: 3. The name can be the vertex of the angle: G. Finally, the name can be a point on one side, the vertex, and a point on the other side of the angle: AGC,CGA. Measuring Angles LESSON 1-6 Additional Examples Name the angle below in four ways. Quick Check

  2. Use a protractor to measure each angle. m 1 = 110 Because 90 < 110 < 180, 1 is obtuse. m 2 = 80 Because 0 < 80 < 90, 2 is acute. Measuring Angles LESSON 1-6 Additional Examples Find the measure of each angle. Classify each as acute, right, obtuse, or straight. Quick Check

  3. m 1 + m 2 = m ABCAngle Addition Postulate. 42 + m 2 = 88Substitute 42 for m 1 and 88 for m ABC. m 2 = 46 Subtract 42 from each side. Measuring Angles LESSON 1-6 Additional Examples Suppose that m 1 = 42 and m ABC = 88. Find m 2. Use the Angle Addition Postulate to solve. Quick Check

  4. Two angles are supplementary if the sum of their measures is 180. A straight angle has measure 180, and each pair of adjacent angles in the diagram forms a straight angle. So these pairs of angles are supplementary: 1 and 2, 2 and 3, 3 and 4, and 4 and 1. Measuring Angles LESSON 1-6 Additional Examples Name all pairs of angles in the diagram that are: a. vertical Vertical angles are two angles whose sides are opposite rays. Because all the angles shown are formed by two intersecting lines, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. b. supplementary

  5. Measuring Angles LESSON 1-6 Additional Examples (continued) c. complementary Two angles are complementary if the sum of their measures is 90. No pair of angles is complementary. Quick Check

  6. 3 and 5 are not marked as congruent on the diagram. Although they are opposite each other, they are not vertical angles. So you cannot conclude that 3 5. Measuring Angles LESSON 1-6 Additional Examples Use the diagram below. Which of the following can you conclude: 3 is a right angle, 1 and 5 are adjacent, 3 5? You can conclude that 1 and 5 are adjacent because they share a common side, a common vertex, and no common interior points. Although 3 appears to be a right angle, it is not marked with a right angle symbol, so you cannot conclude that 3 is a right angle. Quick Check

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