zMath 180  - Unit 13: Polygons
Refer to polygon ABCDEF and complete the following activity, then answer the first four questions. One diagonal is drawn from points F to C. Add more diagonals that do not overlap; in other words, the lines do not cross each other. Copy the figure or print it to paper to draw all possible non-overlapping diagonals.

1) Using two letters for each segment, name the other diagonals that you drew.

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2) With the addition of the extra diagonals in the previous problem, the hexagon is divided into how many triangles?

3) How many degrees do the angles in one triangle total?

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4) To find the number of degrees that the interior angles of a hexagon total, multiply the number of triangles determined in your drawing times 180. How many degrees do the interior angles of a hexagon total?

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Print out or sketch the table shown below. Complete each part of the table. Use the polygons that are below the table to determine the number of triangles that can be drawn using non-overlapping diagonals to connect the vertices in each polygon. After completing the table, answer the next four questions.

5) What is the sum of the interior angles of (a) the square, (b) the pentagon, and (c) the octagon?

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6) Let “n” represent the number of sides of any polygon and write an expression to represent the number of triangles that an n-gon can be divided into by using non-overlapping diagonals. (Hint: For each shape in the table, compare the number of sides in the polygon to the number of triangles, look for a pattern, and then write the expression.)

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7) Use the expression in the previous problem to state a formula to determine the sum of the interior angles in an n-gon. (Hint: Recall the sum of the angles in a triangle.)

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8) Each of the figures represented in the table are regular polygons; that is, they are polygons that have all sides and all angles congruent. What is the measure of one interior angle of (a) a square, (b) a pentagon, and (c) an octagon?

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9) What is the measure of an interior angle of a regular hexagon?

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10) What is the measure of an interior angle of an equilateral triangle?

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11) True or False. The sum of an interior angle of a polygon and its exterior angle is 180 degrees.

12) Find the measure of an exterior angle formed at any of the vertices of a regular pentagon.

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13) What is the sum of the exterior angles of a pentagon?

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14) Find the sum of the exterior angles of a square.

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15) Find the sum of the exterior angles of a decagon.

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Review

Refer to the chart below to change the standard measure to metric measure.

16) 5 in = ______ cm

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17) 4 mi = ______ km

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18) 8 lb = ______ kg (Round to nearest tenth.)

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19) 2 c = ______ ml

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20) What is the square root to the nearest tenth?

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21) What is the square root to the nearest tenth?

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22) Simplify.

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23) Simplify.

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24) Simplify.

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25) Solve for “x”.

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26) Solve for “x”.

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27) Solve for “x”. (Hint: The answer is a fraction.)

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28) Simplify.

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29) Simplify.

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30) Simplify.

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31) Draw and label ray ST on paper. Draw and label ray TS on paper. Does the sketch and labeling of ray ST represent the same ray as the sketch and labeling of ray TS?

32) Draw and label line PR on paper. Draw and label line RP on paper. Does the sketch and labeling of line PR represent the same line as the sketch and labeling of line RP?

Refer to the figure of parallel lines "k" and "t" cut by transversal "m" shown below to answer the next seven problems.

33) Name all angles congruent to angle 1.

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34) Name all angles congruent to angle 2.

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35) Name one pair of vertical angles.

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36) Name one pair of corresponding angles.

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37) Name one pair of alternate interior angles.

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38) Name a pair of supplementary angles.

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39) Look carefully and make a statement concerning the relationship and/or size that is true about the alternate exterior angles; that is, angles 1 and 7 and also angles 2 and 8 (located in the exterior of the parallel lines and on opposite sides of the transversal.)

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40) Given the information in the figure shown, what is the measure of "angle m" in triangle PQR?

41) Integer or Irrational?

42) Identify the number as integer, rational, and/or irrational. There may be more than one answer.

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43) Solve for “x”.

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44) Which inequality represents the solution for the given inequality?

45) List the integers that could be substituted for “n” in the inequality given in the previous problem that would make the inequality a true statement. Choose from –10 through 10.

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