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1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown:

(a) Suppose a car is traveling west on 4th Street and turns onto King Avenue heading south. What is the measure of the angle created by the car's turning? Explain your answer.

(b) Suppose a car is traveling southwest on King Avenue and turns right onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.

(c) Suppose a car is traveling northeast on King Avenue and turns right onto 4th Street. What is the measure of the angle created by the car's turning? Explain your answer

1 All numbered streets runs parallel to each other Both 3rd and 4th Streets are intersected by King Ave as shown a Suppose a car is traveling west on 4th Street class=

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Answer:

(a) 105°

(b) 75°

(c) 105°

Step-by-step explanation:

According to the options, we have,

(a) The car is travelling west on the 4th street and turns towards south on King Avenue.

So the angle (a) will be the angle made by the car's turning.

As, ∠(a) + 75° = 180°

i.e. ∠(a) = 180° - 75°

i.e. ∠(a) = 105°

(b) The car is travelling southwest on the King Avenue and turns right onto 3rd street.

So the angle (b) will be the angle made by the car's turning.

As, 3rd and 4th street are parallel. So, the corresponding angles have equal measures.

Thus, ∠(b) = 75°

(c) The car is travelling northeast on the King Avenue and turns right onto 4th street.

So the angle (c) will be the angle made by the car's turning.

As, ∠(c) + 75° = 180°

i.e. ∠(c) = 180° - 75°

i.e. ∠(c) = 105°

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The angles created by the car as it turns from 4th street into King Avenue to 3rd street are;

(a) 105°

(b) 75°

(c) 75°

What methods can be used to find the angle created by the turning of the car?

The given parameter are;

3rd and 4th streets are parallel to each other.

Two parallel lines having a common transversal, have the following properties.

  • Adjacent angles are supplementary
  • Corresponding angles are equal

Vertically opposite angles are (always) equal

(a) The direction the car travels, west then south on King Avenue makes an adjacent angle with the given angle of 75°.

Adjacent angles are supplementary

The direction of turning of the car is a supplementary angle to the angle 75°

Therefore;

The direction the car turns = 180° - 75° = 105°

(b) A car travelling southwest on King Avenue then turns right on 3rd street turns at an angle corresponding to the given angle 75°

Corresponding angles are equal

Therefore;

The angle turned by the car is 75°

(c) A car traveling northeast on King Avenue then turns right onto 4th street creates an angle that is vertically opposite to the given angle of 75°

Therefore;

The angle created by the car is 75°

Learn more about angles formed by two parallel lines having a common transversal here:

https://brainly.com/question/1751268

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