When a line (transversal) intersects two parallel lines in the same plane, eight angles are formed. In this article, we will teach you how to find the missing angles in this case by using the Parallel Lines and Transversals rules.
• Angles 1 and 8
• Angles 2 and 7
• Angles 3 and 6
• Angles 4 and 5
In the following diagram, two parallel lines are cut by a transversal. What is the value of \(x\)?
Solution:
The two angles \(3x-15\) and \(2x+7\) are equivalent.
That is: \(3x-15=2x+7\)
Now, solve for \(x: 3x-15+15=2x+7+15 →\)
\(3x=2x+22→3x-2x=2x+22-2x→x=22\)
In the following diagram, two parallel lines are cut by a transversal. What is the value of \(x\)?
Solution:
The two angles \(75^\circ\) and \(11x-2\) are equal. \(11x-2=75\)
Now, solve for \(x: 11x-2+2=75+2→ 11x=77→x=\frac→x=7\)
In the following diagram, two parallel lines are cut by a transversal. What is the value of \(x\)?
Solution:
The two angles \(7x-35\) and \(3x+45\) are equivalents.
That is: \(7x-35=3x+45\)
Now, solve for \(x: 7x-35+35=3x+45+35 →\)
\(7x=3x+80→7x-3x=3x+80-3x→4x=80→x=\frac→x=20\)
In the following diagram, two parallel lines are cut by a transversal. What is the value of \(x\)?
Solution:
The two angles \(3x-27\) and \(-x+33\) are equivalents.
That is: \(3x-27=-x+33\)
Now, solve for \(x: 3x-27+27=-x+33+27 →\)
\(3x=-x+60→3x+x=-x+60+x→4x=60→x=\frac→x=15\)