Question

1. ∠2 is the complement of ∠3, and m∠2 = 24°. find m∠3.

a. 66° b. 48° c. 156° d. 24°

1. ∠3 is the supplement of ∠2, and m∠3 = 76°. find m∠2.

a. 104° b. 152° c. 76° d. 14°

1. what is the measure of x in the diagram?

a. 113 degrees b. 157 degrees c. 23 degrees d. 67 degrees

1. which construction is demonstrated in the figure to the right?

a. angle bisector b. copy an angle c. perpendicular bisector d. copy a line segment

1. evaluate: - 4 + 6-(-3)-1 + 2+(-9)-7
2. solve the equation below.

5x - 2=-3x - 18

1. why is it important to start with the smaller variable term when solving equations with variables on both sides of the equation?
2. explain the difference between ab and \\(\overline{ab}\\).

Explanation:

Step1: Solve problem 11

Complementary angles sum to 90°. If ∠2 is the complement of ∠3 and m∠2 = 24°, then m∠3=90° - 24° = 66°.

Step2: Solve problem 12

Supplementary angles sum to 180°. If ∠3 is the supplement of ∠2 and m∠3 = 76°, then m∠2=180° - 76° = 104°.

Step3: Solve problem 13

The angle adjacent to 67° and x are complementary. So x = 90° - 67°=23°.

Step4: Solve problem 14

The figure shows the construction of a perpendicular bisector.

Step5: Solve problem 16

-4 + 6-(-3)-1 + 2+(-9)-7=-4 + 6 + 3-1 + 2-9-7=( - 4-1-9-7)+(6 + 3+2)=-21 + 11=-10.

Step6: Solve problem 17

5x - 2=-3x - 18. Add 3x to both sides: 5x+3x - 2=-3x+3x - 18, 8x - 2=-18. Add 2 to both sides: 8x-2 + 2=-18 + 2, 8x=-16. Divide both sides by 8: x=-2.

Step7: Solve problem 18

Starting with the smaller variable - term when solving equations with variables on both sides can simplify the process by reducing the number of negative - coefficient terms and making the arithmetic operations easier. For example, if we have 3x+5 = 2x + 7, subtracting 2x from both sides first gives x+5 = 7, which is easier to solve than subtracting 3x from both sides first.

Step8: Solve problem 19

AB usually represents a line - segment with endpoints A and B. $\overline{AB}$ also represents the line - segment with endpoints A and B. There is no difference in standard geometric notation; sometimes $\overline{AB}$ is used to emphasize it is a line - segment while AB can be used more casually in text to refer to the line - segment between A and B.

Answer:

1. 66°
2. A. 104°
3. C. 23 degrees
4. C. Perpendicular Bisector
5. - 10
6. x=-2
7. Simplifies the solving process by reducing negative - coefficient terms.
8. There is no real difference; both represent the line - segment between A and B.