Three houses are mapped on a coordinate grid.
Josh’s house is located on Red Street at (7, 6).
Sarah’s house is located on Green Street at (-8,-5).
Emma’s house is located on the corner of Red Street and Green Street at (-2,-4).
What is the measure of the angle (in degrees) where Red Street and the Green Street intersect

According to Geometry, a line is generated by two distinct points on a plane and an angle by two distinct lines on a plane. In this case, we need to generate the angle associated with Red Street and Green Street. This can be found by using the definition of dot product:

u • v = |u| · |v| · cos θ (1)

Where θ is the angle generated by the two streets.

Now we determine the vectors and its magnitude:

u = (7, 6) - (- 2, - 4)

u = (9, 10)

|u| = √(9² + 10²)

|u| = √181

v = (- 8, - 5) - (- 2, - 4)

v = (- 6, - 1)

|v| = √[(- 6)² + (- 1)²]

|v| = √37

Finally, we find the measure of the angle:

u • v = (9, 10) • (- 6, - 1)

u • v = - 54 - 10

u • v = - 64

cos θ = (- 64) / (√181 · √37)

θ ≈ 141.450°

The measure of the angle where Red Street and Green Street intersect is approximately 141.450°.

To learn more on dot products: https://brainly.com/question/17039901

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