Answer:
x = 18, y = 6
Step-by-step explanation:
Given the two parallel lines cut through by a transversal, thereby creating perpendicular lines. According to the Perpendicular Transversal Theorem, if a transversal is perpendicular to one of the parallel lines, then it means that the same transversal must also be perpendicular to the other parallel line.
Since perpendicular lines form 90° angles, then it means that each of the angles formed by the intersection of the parallell lines and transversal has a measure of 90°.
Thus, we can infer that (3x + 6y)° = 90°, and (5x)° = 90°.
Solve for x:
Start by dividing both sides by 5 to solve for x:
5x° = 90°
[tex]\large\mathsf{\frac{\:5x^{\circ}}{5}\:=\:\frac{\:90^{\circ}}{5}}[/tex]
x = 18°
Solve for y:
Substitute the value of x into the (3x + 6y)° to solve for y:
3x° + 6y° = 90°
3(18)° + 6y = 90°
54° + 6y° = 90°
Subtract 54° from both sides:
54° - 54° + 6y° = 90° - 54°
6y° = 36°
Divide both sides by 6 to solve for y:
[tex]\large\mathsf{\frac{\:6y^{\circ}}{6}\:=\:\frac{\:36^{\circ}}{6}}[/tex]
y = 6°
Answers:
Therefore, x = 18, and y = 6.
