Question

14)
17x - 4
12 + 15x
relationship:
congruent or supplementary?
equation:
x =
15)
a
x + 75
x + 125
relationship:
congruent or supplementary?
equation:
x =
16)
-1 + 14x
12x + 17
relationship:
congruent or supplementary?
equation:
x =
17)
8x - 8
6x + 14
relationship:
congruent or supplementary?
equation:
x =
18)
16x - 1
15x + 5
relationship:
congruent or supplementary?
equation:
x =
19)
5x + 10
16x + 2
relationship:
congruent or supplementary?
equation:
x =
20)
-4 + 9x
7x + 8
relationship:
congruent or supplementary?
equation:
x =
21)
58 + x
138 + x
relationship:
congruent or supplementary?
equation:
x =
22)
13x + 3
14x - 6
relationship:
congruent or supplementary?
equation:
x =

Explanation:

14.)

Step1: Identify relationship

The angles are corresponding angles, so they are congruent.

Step2: Set up equation

$17x - 4 = 12 + 15x$

Step3: Solve for x

$17x - 15x = 12 + 4$
$2x = 16$
$x = 8$

15.)

Step1: Identify relationship

The angles are same-side interior angles, so they are supplementary.

Step2: Set up equation

$(x + 75) + (x + 125) = 180$

Step3: Solve for x

$2x + 200 = 180$
$2x = 180 - 200$
$2x = -20$
$x = -10$

16.)

Step1: Identify relationship

The angles are alternate exterior angles, so they are congruent.

Step2: Set up equation

$-1 + 14x = 12x + 17$

Step3: Solve for x

$14x - 12x = 17 + 1$
$2x = 18$
$x = 9$

17.)

Step1: Identify relationship

The angles are alternate interior angles, so they are congruent.

Step2: Set up equation

$8x - 8 = 6x + 14$

Step3: Solve for x

$8x - 6x = 14 + 8$
$2x = 22$
$x = 11$

18.)

Step1: Identify relationship

The angles are corresponding angles, so they are congruent.

Step2: Set up equation

$16x - 1 = 15x + 5$

Step3: Solve for x

$16x - 15x = 5 + 1$
$x = 6$

19.)

Step1: Identify relationship

The angles are same-side exterior angles, so they are supplementary.

Step2: Set up equation

$(5x + 10) + (16x + 2) = 180$

Step3: Solve for x

$21x + 12 = 180$
$21x = 180 - 12$
$21x = 168$
$x = 8$

20.)

Step1: Identify relationship

The angles are alternate interior angles, so they are congruent.

Step2: Set up equation

$-4 + 9x = 7x + 8$

Step3: Solve for x

$9x - 7x = 8 + 4$
$2x = 12$
$x = 6$

21.)

Step1: Identify relationship

The angles are same-side interior angles, so they are supplementary.

Step2: Set up equation

$(58 + x) + (138 + x) = 180$

Step3: Solve for x

$2x + 196 = 180$
$2x = 180 - 196$
$2x = -16$
$x = -8$

22.)

Step1: Identify relationship

The angles are same-side interior angles, so they are supplementary.

Step2: Set up equation

$(13x + 3) + (14x - 6) = 180$

Step3: Solve for x

$27x - 3 = 180$
$27x = 180 + 3$
$27x = 183$
$x = \frac{61}{9} \approx 6.78$

Answer:

14.) Relationship: Corresponding Angles (Congruent); Equation: $17x - 4 = 12 + 15x$; $x=8$
15.) Relationship: Same-Side Interior Angles (Supplementary); Equation: $(x + 75) + (x + 125) = 180$; $x=-10$
16.) Relationship: Alternate Exterior Angles (Congruent); Equation: $-1 + 14x = 12x + 17$; $x=9$
17.) Relationship: Alternate Interior Angles (Congruent); Equation: $8x - 8 = 6x + 14$; $x=11$
18.) Relationship: Corresponding Angles (Congruent); Equation: $16x - 1 = 15x + 5$; $x=6$
19.) Relationship: Same-Side Exterior Angles (Supplementary); Equation: $(5x + 10) + (16x + 2) = 180$; $x=8$
20.) Relationship: Alternate Interior Angles (Congruent); Equation: $-4 + 9x = 7x + 8$; $x=6$
21.) Relationship: Same-Side Interior Angles (Supplementary); Equation: $(58 + x) + (138 + x) = 180$; $x=-8$
22.) Relationship: Same-Side Interior Angles (Supplementary); Equation: $(13x + 3) + (14x - 6) = 180$; $x=\frac{61}{9}$