Given one angle is 65°, find x and y
When two parallel lines are crossed by a third line — called a transversal — special pairs of equal angles appear. Let's find some!
First, two parallel lines. The little arrows show they run in the same direction and never meet.
Now we add a transversal — a line that cuts across both parallel lines.
We're told that this angle right here measures sixty-five degrees.
Down at the second crossing, there's an angle marked x. Can we figure out its measure?
These two angles sit between the parallel lines, on opposite sides of the transversal. That makes them alternate interior angles.
And here's the big rule: alternate interior angles are always equal!
So x must also equal sixty-five degrees.
Now look at angle y — it's right next to x, on the same side of the transversal as our sixty-five.
Y and the sixty-five are co-interior angles. Co-interior angles always add up to one hundred eighty degrees.
So y equals one hundred eighty minus sixty-five — which is one hundred fifteen degrees.
Great work! x is sixty-five degrees, and y is one hundred fifteen. Parallel lines turn angle hunting into a puzzle you can solve.