The value of the equations related to the angle system related to the two parallel lines (avenues A and B) cut by a third diagonal line (avenue C) is equal to to 12.
How to determine the value of x from a system of angles
In this question we must apply all Euclidean theorems of angles between two parallel lines cut by a third diagonal line. The internal angle between avenues B and C equals 6 · x - 18 and the external angle between avenues A and C equals 10 · x + 6.
By alternate internal angles between parallel lines we infer the measure of the internal angle between the avenues A and C equals 6 · x - 18, and definition of supplementary angles we have the following expression:
(6 · x - 18) + (10 · x + 6) = 180
16 · x - 12 = 180
16 · x = 192
x = 12
The value of the equations related to the angle system related to the two parallel lines (avenues A and B) cut by a third diagonal line (avenue C) is equal to to 12. [tex]\blacksquare[/tex]
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