Question

city engineering seventh avenue runs perpendicular to 1st and 2nd streets, which are parallel. however, maple avenue makes a 115° angle with 2nd street. what is the measure of angle 1?

Explanation:

Step1: Use the property of corresponding angles

Since 1st and 2nd Streets are parallel, the angle corresponding to the 115 - degree angle with respect to the transversal (Maple Avenue) has the same measure of 115 degrees.

Step2: Consider the right - angle formed by 7th Avenue

7th Avenue is perpendicular to 1st and 2nd Streets, creating right - angles. Let the angle we want to find be $\angle1$. We know that the sum of the angle formed by 7th Avenue and Maple Avenue and $\angle1$ is equal to the corresponding 115 - degree angle. Since the angle between 7th Avenue and Maple Avenue along 1st Street is a right - angle (90 degrees), we can find $\angle1$ by subtracting 90 degrees from 115 degrees.
$115^{\circ}-90^{\circ}=25^{\circ}$

Answer:

$25^{\circ}$