4.7 Angles and Angle Measurement

Unit Goals

  • Students learn to draw and identify points, rays, segments, angles, and lines, including parallel and perpendicular lines. Students also learn how to use a protractor to measure angles and draw angles of given measurements, and identify acute, obtuse, right, and straight angles in two-dimensional figures.

Section A Goals

  • Draw and identify points, lines, rays, segments, and parallel and intersecting lines in geometric figures.
  • Recognize that angles are formed wherever two rays share a common endpoint and identify angles in two-dimensional figures.

Section B Goals

  • Recognize that angles can be measured in degrees, and can be found using addition and subtraction.
  • Use a protractor to measure and draw angles, and recognize that perpendicular lines meet or cross at a right angle.

Section C Goals

  • Draw and identify acute, obtuse, right, and straight angles in two-dimensional figures.
  • Write equations to represent angle relationships and reason about and find unknown measurements.
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Glossary Entries

  • acute angle
    An angle that measures less than 90 degrees.

  • angle
    A figure made up of two rays that share the same endpoint.

  • common denominator
    The same denominator in two or more fractions. For instance, \(\frac{1}{4}\) and \(\frac{5}{4}\) have a common denominator.

  • composite number
    A whole number with more than 1 factor pair.

  • denominator
    The bottom part of a fraction that tells how many equal parts the whole was partitioned into.

  • dividend
    The number being divided. For example, when 37 is divided by 5, we call 37 the dividend. 

  • equivalent fractions
    Fractions that have the same size and describe the same point on the number line. For example, \(\frac{1}{2}\) and \(\frac{2}{4}\) are equivalent fractions.

  • factor pair of a whole number
    A pair of whole numbers that multiply to result in that number. For example, 5 and 4 are a factor pair of 20.

  • intersecting lines
    Lines that cross.

  • line

    A set of points that are arranged in a straight way and extend infinitely in opposite directions.

  • mixed number
    A number expressed as a whole number and a fraction less than 1. 

  • multiple of a number
    The result of multiplying that number by a whole number. For example, 18 is a multiple of 3, because it is a result of multiplying 3 by 6.

  • numerator

    The top part of a fraction that tells how many of the equal parts are being described.

  • obtuse angle
    An angle that measures greater than 90 degrees.

  • parallel lines
    Lines that never intersect.

  • perpendicular lines
    Lines that intersect creating right angles.

  • point

    A location along a line or in space.

  • prime number
    A whole number that is greater than 1 and has exactly one factor pair: the number itself and 1.

  • ray
    A line that ends at one point and goes on in the other direction.

  • remainder
    The number left over when we take away as many equal groups as we can from a number. 

  • right angle
    An angle with a measurement of 90 degrees.

  • rounding

    A formal way to say which number a given number is closer to. For example, for 182, the number 180 is the closest multiple of ten and 200 is the closest multiple of a hundred. We can round 182 to 180 (if rounding to the nearest ten) or 200 (if rounding to the nearest hundred).

  • segment or line segment

    A part of a line with two endpoints.

  • straight angle
    An angle that measures 180 degrees.

  • vertex
    The point where the two rays meet.