SOLUTION: A pair of congruent angles are described as follows the degree measures of one angle is three more than twice a number and the other angles degree measures is 54.5 less than three

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Question 1058070: A pair of congruent angles are described as follows the degree measures of one angle is three more than twice a number and the other angles degree measures is 54.5 less than three times the number determine the measures of the angles in degrees
Answer by solve_for_x(190) About Me  (Show Source):
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Let x represent the number.

The measure of the first angle is then 2x + 3.

The measure of the second angle is 3x - 54.5.

Since the two angles are congruent, their measures must be equal, which gives:

3x - 54.5 = 2x + 3

3x - 2x - 54.5 = 3

x - 54.5 = 3

x = 3 + 54.5

x = 57.5

The measures of the two angles are then:

First angle = 2(57.5) + 3 = 118 degrees

Second angle (as a check) = 3(57.5) - 54.5 = 118 degrees

Solution: The angles each measure 118 degrees.