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How to Find the Measure of Angles in Shapes With Parallel Lines

Geometric shapes (figures) sometimes have one or more sets of parallel lines. Parallel lines remain equidistant (the same distance apart). These figures have angles (the amount of turn on a 360-degree scale) between adjacent sides. Angles are measured inside the figure in a scale called degrees.

Things You'll Need

  • Protractor
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Instructions

  1. Measuring the Angles of Squares and Rectangles

    • 1

      Mark the four angles in the square or rectangle, using the symbol for a right (90 degrees) angle (square). Right angles are always 90 degrees and look like corners. The symbol should fit in the interior of each angle and always identifies the angle as a right angle. Squares are a type of rectangle where all four sides are the same length. Squares and rectangles both have four, interior, right angles that add up to 360 degrees.

    • 2

      Mark each side of a square using a short, single line (|) drawn perpendicular to, and through, the center of each side to indicate all four sides are equal in length. Mark two parallel sides of a rectangle with a short, single line (|) drawn perpendicular to, and through, the center of each side to indicate these two sides are of equal length. On the two remaining parallel sides, draw two, short lines (||) perpendicular to, and through, the center of each side to indicate these two sides are of equal length.

    • 3

      Measure all four angles of squares or rectangles. One angle at a time, line up the protractor's baseline along one arm (side) of the angle, placing the center of the protractor's baseline in the vertex (corner) of the angle. Starting from 0 degrees, follow around the scale of the protractor to the point where the other arm of the angle crosses the scale. Read the angle in degrees. Each angle is 90 degrees. Since the right angle symbol (square) means the angle is 90 degrees, the angles does not need to be labeled by writing 90 degrees.

    Measuring Angles of a Rhombus, Parallelogram and Trapezoids

    • 4

      Mark the sides of equal length for each figure. A rhombus is a geometric figure where all four sides of the figure are of equal length. A parallelogram has two sets of parallel lines, with each set a different length. If the trapezoid has two sides that are equal in length, it is an isosceles trapezoid. Other trapezoids have no equal sides. Use a short, single line (|) drawn perpendicular to, and through, the center of two equal sides to indicate they are equal in length. On the two remaining parallel sides, draw two, short lines (||) perpendicular to, and through, the center of each side to indicate these two sides are of equal length.

    • 5

      Draw an arc between adjacent line segments, inside each angle. Opposite angles in a rhombus and a parallelogram are equal. If the figure is an isosceles trapezoid, the two angles along the base of the figure are equal and the two angles at the top of the figure are equal. Other trapezoids will not have any angles of equal size.

    • 6

      Label two opposite angles "a", and the other two opposite angles "b" in a rhombus, parallelogram or isosceles trapezoid. Add an extra arc, parallel to the first arc, in both "b" angles. Label angles in other trapezoids "a", "b", "c" and "d".

    • 7

      Measure one angle "b" of a figure by lining up the protractor's baseline with one arm of the angle. Align the center of the protractor baseline with the vertex of the angle. Starting from 0 degrees, follow around the scale of the protractor to the point where the other arm of the angle crosses the scale. Read the angle in degrees. Label both angles marked "b" with the degree reading. Measure, and mark, the remaining angles of other trapezoids in the same manner.

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