On a city map, Pine Street and Oak Street are parallel. A straight footpath crosses Pine Street, forming an angle of with Pine Street.
At the point where the same footpath crosses Oak Street, the obtuse angle formed by the footpath and Oak Street is labeled .
Which choice is the value of ? (All angle measures are in degrees.)
A transversal is a line that crosses two lines. If those lines are parallel, angles in matching positions at the crossings are equal. Find the matching angle first, then check whether the requested angle is beside it on a straight line. Don't copy an acute angle into a spot marked obtuse.
Hints
- Hint 1
A corresponding angle sits in the same position at each crossing of two parallel lines. Find the angle at Oak between its rightward ray and the footpath ray going down and right. What measure does it have?
- Hint 2
A linear pair is two side-by-side angles that form a straight line, so they add to . The labeled angle is obtuse, not the matching acute angle. Which angle sits beside it at Oak?
Step-by-step
Match the acute angle, then use a straight line
Step 1Find the matching angle at Oak
No Desmos needed. Parallel-line angles and one subtraction give the answer. The footpath is a transversal, a line crossing both streets. Because the streets are parallel, the angle at Oak between its rightward ray and the footpath ray going down and right matches the angle at Pine. It also measures .
- Step 2
Make the straight-angle equation
Only one angle sits beside at Oak. Their footpath rays point in opposite directions, so the two angles form a linear pair: together, they make a straight angle of .
- Step 3
Find the obtuse angle
Subtract from both sides:
Evaluate the subtraction:
So the obtuse angle at Oak Street measures . Choice A.