Question

Nolan Street runs east to west across town. Gevers Street intersects Nolan Street from the north. The angle at the northwest corner of Nolan and Gevers Street measures 45 degrees. What is the measure of the angle at the northeast corner?

A. 180 degrees
B. 135 degrees
C. 45 degrees
D. 150 degrees

Answer 1

The angle at the northeast corner of Nolan and Gevers Street is 45 degrees, found by subtracting 45 degrees (the angle at the northwest corner) from 90 degrees (a right angle).

Step-by-step explanation:

The student is asking to find the measure of the angle at the northeast corner of the intersection. We know Nolan Street runs east to west, and Gevers Street intersects from the north, forming an angle of 45 degrees at the northwest corner. Since streets intersect at right angles, or 90 degrees, we can infer that each corner of the intersection also forms a 90-degree angle. Therefore, the intersection resembles a square or rectangle, and the angles at each corner would total 360 degrees.

We can find the measure of the angle at the northeast corner by subtracting the known angle from 90 degrees. Since the northwest corner is 45 degrees, we subtract this from 90 degrees to find that the northeast corner is 45 degrees as well: 90 degrees - 45 degrees = 45 degrees. Thus, the correct answer is C. 45 degrees.