The solution of the system of linear equations behind the geometric system is (x, z) = (29, 13). The measures of the angles RIG and ZIM are 59° and 140°, respectively.
What are the variables behind a geometric system formed by three lines?
In this problem we find a geometric system generated by lines GZ, AM and IR, in which two variables are shown (x, z) and whose values can be found by applying the concepts of complementary and supplementary angles.
A group of angles are complementary if the sum of their measures equals 90°, and supplementary if that sum equals 180°. This system can be represented by the following system of linear equations:
(3 · x - 56) + 90 + (4 · z + 7) = 180 (1)
(4 · z + 7) + (x + 2) = 90 (2)
By (1):
(3 · x - 56) + (4 · z + 7) = 90
3 · x + 4 · z - 49 = 90
3 · x + 4 · z = 139 (1b)
By (2):
x + 4 · z = 81 (2b)
The solution of the system of linear equations behind the geometric system is (x, z) = (29, 13).
Then, the measures of the angles RIG and ZIM are, respectively:
m ∠ RIG = 4 · z + 7
m ∠ RIG = 4 · 13 + 7
m ∠ RIG = 59°
m ∠ ZIM = 360° - (3 · x - 56) - 90° - (4 · z + 7) + (x + 2)
m ∠ ZIM = 360 - 3 · 29 - 56 - 90 - 4 · 13 + 7 + 29 + 2
m ∠ ZIM = 140°
The measures of the angles RIG and ZIM are 59° and 140°, respectively.
To learn more on supplementary angles: https://brainly.com/question/18164299
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