Subjects geometry

Angle Relationships

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Angle Relationships


1. **State the problem:** We are given a diagram with streets Maple Ave, 7th Ave, 2nd St, and 1st St intersecting. We know the angle between Maple Ave and 2nd St is 115°. 2. **Find the angle of Maple Ave:** Maple Ave is diagonal, and the angle between Maple Ave and 2nd St (horizontal) is 115°. Since 2nd St is horizontal, the angle Maple Ave makes with the horizontal is 115°. 3. **Find the angle of 2nd St:** 2nd St is horizontal, so its angle with the horizontal axis is 0°. 4. **Find the angle of 1st St:** 1st St is parallel to 2nd St (both horizontal), so its angle is also 0°. 5. **Find the value of angle 1:** Angle 1 is between 2nd St and 1st St, which are parallel lines, and the transversal is 7th Ave (vertical). The angle between horizontal and vertical lines is 90°. Since angle 1 is below 2nd St and above 1st St, it is the angle between the horizontal and vertical lines, so angle 1 = 90°. **Final answers:** - Angle of Maple Ave = $115^\circ$ - Angle of 2nd St = $0^\circ$ - Angle of 1st St = $0^\circ$ - Angle 1 = $90^\circ$