Question

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

Answer 1

The measure of the angle created by the car's turning is 105°

Step-by-step explanation:

  Given :  a car is traveling east on 4th Street and turns onto King Avenue heading northeast.

We have to calculate the measure of the angle created by the car's turning.

Since, car is travelling in east direction on 4th street that is from A to D as shown below in image by arrow.

Then at point B, the car turns toward King Avenue heading northeast. that is B to C as shown below in image

Since, we need to calculate  the measure of the angle created by the car's turning that is measure of ∠ABC.

AD is a straight line, thus measure of any angle  at line segment AD is 180° as angles on one side of a straight line always add to 180 degrees

Therefore, at B,

∠ABC + ∠CBD = 180°

Aldo given , ∠CBD = 75°

Thus, the measure of ∠ABC is ,

⇒ ∠ABC  = 180° -∠CBD

⇒ ∠ABC  = 180° - 75°

⇒ ∠ABC  = 105°

Thus, the measure of the angle created by the car's turning is 105°