B Apply

Algebra Find the values of the variables.

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21. Think About a Plan People in ancient Rome played a game called terni lapilli. The exact rules of this game are not known. Etchings on floors and walls in Rome suggest that the game required a grid of two intersecting pairs of parallel lines, similar to the modern game tick-tack-toe. The measure of one of the angles formed by the intersecting lines is 90 ° . 90 degrees .  Find the measure of each of the other 15 angles. Justify your answers.
    • How can you use a diagram to help?
    • You know the measure of one angle. How does the position of that angle relate to the position of each of the other angles?
    • Which angles formed by two parallel lines and a transversal are congruent? Which angles are supplementary?

22. Error Analysis Which solution for the value of x in the figure below is incorrect? Explain.

    

    1. 2 x = x + 75 x = 75 table with 2 rows and 2 columns , row1 column 1 , 2 x , column 2 equals x plus 75 , row2 column 1 , x , column 2 equals 75 , end table
    2. 2 x + ( x + 75 ) = 180 3 x + 75 = 180 3 x = 105 x = 35 table with 4 rows and 2 columns , row1 column 1 , 2 x plus . open , x plus 75 , close , column 2 equals 180 , row2 column 1 , 3 x plus 75 , column 2 equals 180 , row3 column 1 , 3 x , column 2 equals 105 , row4 column 1 , x , column 2 equals 35 , end table

23. Outdoor Recreation Campers often use a “bear bag” at night to avoid attracting animals to their food supply. In the bear bag system below, a camper pulls one end of the rope to raise and lower the food bag.

    

    1. Suppose a camper pulls the rope taut between the two parallel trees, as shown. What is m ∠ 1 ? m angle 1 question mark
    2. Are ∠ 1 angle 1  and the given angle alternate interior angles, same-side interior angles, or corresponding angles?
24. Writing Are same-side interior angles ever congruent? Explain.

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