Question

Graded Assignment Unit Test, Part 2: Basic Geometric Shapes Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit. Total score: ____ of 15 points (Score for Question 1: ___ of 3 points) 1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown: a. Hint: Think about it from the car’s perspective. The angle you’re finding is the inside angle of the car’s turn. (a) Suppose a car is traveling east on 4th Street and turns onto King Avenue heading northeast. 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 left 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 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.

Answer 1

Answer:

In case (a) car makes 105° turn.

In case (b) car makes 75° turn.

In case (c) car makes 105° turn.

Step-by-step explanation:

Figure is redrawn To explain properly (in attachment)

Given : streets are parallel means $\overline{AB}$ ║ $\overline{CD}$,

             AB - 4th street , CD - 3rd street and XY - King Ave.

            ∠XLA = 75°

To find : (a) ∠XLB

              (b) ∠LMD (left onto 3rd streat means left of car)

              (c) ∠YMD (right means right side of car)

∠XLB + ∠XLA = 180° (Linear Pair = 2 adjacent angles are  

                                     supplementary)

∠XLB + 75° = 180°

∠XLB  = 180 - 75

∠XLB = 105°

∴ In case (a) car makes 105° turn.

∠LMD = ∠XLA = 75° (Corresponding angles of parallel lines are equal)

∠LMD = 75°

∴ In case (b) car makes 75° turn.

∠YMD + ∠LMD = 180° (Linear Pair = 2 adjacent angles are

                                       supplementary)

∠YMD + 75° = 180°

∠YMD = 180 - 75

∠YMD = 105°

∴In case (c) car makes 105° turn.