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: Identify supplementary angle

The 115° angle and its adjacent angle on 2nd St. are supplementary (form a linear pair), so their sum is 180°. Let the adjacent angle be \( x \). Then \( x + 115^\circ = 180^\circ \), so \( x = 180^\circ - 115^\circ = 65^\circ \).

Step2: Use parallel lines (corresponding angles)

1st and 2nd Streets are parallel, and Maple Ave. is a transversal. Angle 1 and the angle \( x \) (65°) are corresponding angles, so they are equal. Thus, angle 1 is 65°.

Answer:

\( 65^\circ \)