Honors Geometry Companion Book, Volume 1

1.1.4 Pairs of Angles (continued)

Translate this sentence into an equation to find the measure of the complement. Dividing the sentence into parts can make the translation easier. First, identify a variable for the unknown. If the unknown is represented by x , then “twice an angle” can be translated to “2 x ,” because “twice” a number means to multiply the number by 2. The next word in the sentence, “measures,” can be translated to “ = ” because if an angle “measures” some number of degrees, that means the angle’s measure is equal to some number of degrees. The next part of the sentence is “9° more than.” The phrase “9 more than” some number is equivalent to 9 plus some number. So, “9° more than” can be translated to “9° + .” The last part of the sentence, “the measure of its complement,” can be translated to (90 − x )°. Put these parts together to form an equation and then solve the equation for x . Remember, x is the measure of the unknown angle, but the answer to this example is the “measure of its complement,” or the measure of the complement of x . So, subtract the value of x , 33°, from 90° to find the answer.


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