The values of x associated with each case are listed below:
- 19
- 11
How to find the variables behind angles in a geometric system
Herein we find two cases of geometric systems generated by two parallel lines and auxiliary line segments, wherein we must use the concept of supplementary angles and triangle properties to determine the value behind angles. Now we proceed to determine the value of the variable x for each case:
Case 1
- m ∠ DCA = m ∠ CBE = 3 · x Alternate internal angles between parallel lines
- m ∠ CAD + m ∠ ADC + m ∠ DCA = 180° Internal angles in triangles
- m ∠ ADC = 180° - 95° = 85° Supplementary angles.
- 2 · x + 85° + 3 · x = 180° Steps 1 & 3
- 5 · x = 95° Algebra
- x = 19 Algebra / Result
Case 2
- m ∠ BFE = 180° - 147° = 33° Supplementary angles
- m ∠ FEB = 180° - 4 · x Supplementary angles
- m ∠ BFE + m ∠ FEB + m ∠ EBF = 180° Internal angles in triangles
- 33° + (180° - 4 · x) + x = 180° Steps 1 & 2
- 3 · x = 33° Algebra
- x = 11 Algebra / Result
To learn more on triangles: https://brainly.com/question/2269348
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