Math Problem Statement

If l || m, solve for x in problems 5 through 8.

Solution

To solve these problems, we will use properties of parallel lines and angles. Specifically, when two lines are parallel, certain angle relationships arise, such as:

  1. Corresponding angles are equal.
  2. Alternate interior angles are equal.
  3. Same-side interior angles are supplementary (sum to 180°).

Let's solve each one:

5.

  • lml \parallel m means that the angles are either corresponding or supplementary.
  • The angle (9x+2)(9x + 2)^\circ and the 119° angle are supplementary (same-side interior angles), so: (9x+2)+119=180(9x + 2) + 119 = 180 9x+121=1809x + 121 = 180 9x=599x = 59 x=5996.56x = \frac{59}{9} \approx 6.56

6.

  • The angles (12x8)(12x - 8)^\circ and 104° are corresponding angles, so they are equal. 12x8=10412x - 8 = 104 12x=11212x = 112 x=11212=9.33x = \frac{112}{12} = 9.33

7.

  • The angles (5x+7)(5x + 7)^\circ and (8x71)(8x - 71)^\circ are alternate interior angles, so they are equal. 5x+7=8x715x + 7 = 8x - 71 7+71=8x5x7 + 71 = 8x - 5x 78=3x78 = 3x x=783=26x = \frac{78}{3} = 26

8.

  • The angles (4x7)(4x - 7)^\circ and (7x61)(7x - 61)^\circ are corresponding angles, so they are equal. 4x7=7x614x - 7 = 7x - 61 617=7x4x61 - 7 = 7x - 4x 54=3x54 = 3x x=543=18x = \frac{54}{3} = 18

Let me know if you'd like further details or explanations. Here are five questions to extend this topic:

  1. How do you determine when angles are supplementary?
  2. What are the differences between corresponding and alternate interior angles?
  3. How can you check if lines are parallel based on angle relationships?
  4. What happens to the angles if the lines are not parallel?
  5. How can transversal lines impact angle calculations in geometric figures?

Tip: When solving angle problems involving parallel lines, always identify whether the angles are corresponding, alternate interior, or supplementary for accurate equation setup.

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Math Problem Analysis

Mathematical Concepts

Parallel Lines
Angle Relationships
Linear Equations

Formulas

Supplementary angles: angle1 + angle2 = 180°
Corresponding angles are equal: angle1 = angle2
Alternate interior angles are equal: angle1 = angle2

Theorems

Angle Sum Theorem
Corresponding Angle Postulate
Alternate Interior Angle Theorem

Suitable Grade Level

Grades 8-10