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.)
When a transversal crosses two parallel lines, first use corresponding (or alternate interior) angles to transfer a known angle measure to the other intersection. Then, if the question asks for an adjacent obtuse angle, use the linear-pair fact that the two adjacent angles sum to .
Hints
Think about a transversal
The footpath crosses both parallel streets, so it acts like a transversal. Corresponding acute angles formed by a transversal with parallel lines are equal.
Identify the acute angle at Oak Street
The acute angle the footpath makes with Oak Street has the same measure as the angle it makes with Pine Street.
Relate acute and obtuse angles at an intersection
At one intersection, an acute angle and its adjacent obtuse angle form a straight line, so they add to .
Desmos Guide
Compute the supplement
In Desmos, enter 180-52.
Interpret the result
The value displayed is the measure of the obtuse angle .
Step-by-step Explanation
Use parallel lines to match the acute angles
Since Pine Street and Oak Street are parallel, the footpath (a transversal) forms equal corresponding acute angles with both streets. So the acute angle between the footpath and Oak Street is .
Use supplementary angles to find the obtuse angle
The obtuse angle at Oak Street and the acute angle form a linear pair, so they sum to :
Therefore, .