Question

name the relationship between ∠1 & ∠2, and then decide whether ∠1 and ∠2 are congruent or supplementary:
7.)
relationship:
congruent or supplementary?
8.)
relationship:
congruent or supplementary?
9.)
relationship:
congruent or supplementary?
name the relationship between ∠y and ∠x, and then decide whether ∠y and ∠x are congruent or supplementary:
10.)
relationship:
congruent or supplementary?
11.)
relationship:
congruent or supplementary?
12.)
relationship:
congruent or supplementary?
name the relationship between the two angles, decide whether the angles are congruent (c) or supplementary (s), set up an equation, and solve for x:
13.)
relationship:
congruent or supplementary?
equation:
x =
11.)
relationship:
congruent or supplementary?
equation:
x =
12.)
relationship:
congruent or supplementary?
equation:
x =
11.)
relationship:
congruent or supplementary?
equation:
x =
12.)
relationship:
congruent or supplementary?
equation:
x =
13.)
relationship:
congruent or supplementary?
equation:
x =

Explanation:

Step1: Identify ∠1 & ∠2 relationship

7.) Relationship: Alternate Exterior Angles
Congruent or Supplementary? Congruent

8.) Relationship: Alternate Interior Angles
Congruent or Supplementary? Congruent

9.) Relationship: Corresponding Angles
Congruent or Supplementary? Congruent

Step2: Identify ∠y & ∠x relationship

10.) Relationship: Alternate Interior Angles
Congruent or Supplementary? Congruent

11.) Relationship: Same-Side Interior Angles
Congruent or Supplementary? Supplementary

12.) Relationship: Corresponding Angles
Congruent or Supplementary? Congruent

Step3: Solve for x (1st set)

13.)

Relationship: Corresponding Angles
Congruent or Supplementary? Congruent
Equation: $8x - 4 = 60$
Solve:
$8x = 60 + 4$
$8x = 64$
$x = \frac{64}{8} = 8$

11.) (duplicate label)

Relationship: Same-Side Interior Angles
Congruent or Supplementary? Supplementary
Equation: $(2x + 43) + (2x - 3) = 180$
Solve:
$4x + 40 = 180$
$4x = 140$
$x = \frac{140}{4} = 35$

12.) (duplicate label)

Relationship: Corresponding Angles
Congruent or Supplementary? Congruent
Equation: $11x - 2 = 75$
Solve:
$11x = 75 + 2$
$11x = 77$
$x = \frac{77}{11} = 7$

Step4: Solve for x (2nd set)

11.) (duplicate label)

Relationship: Same-Side Interior Angles
Congruent or Supplementary? Supplementary
Equation: $(x + 139) + 132 = 180$
Solve:
$x + 271 = 180$
$x = 180 - 271 = -91$

12.) (duplicate label)

Relationship: Vertical Angles (∠CBD) & Corresponding Angles
Congruent or Supplementary? Congruent
Equation: $2x + 60 = 4x$
Solve:
$60 = 4x - 2x$
$2x = 60$
$x = \frac{60}{2} = 30$

13.) (duplicate label)

Relationship: Alternate Interior Angles
Congruent or Supplementary? Congruent
Equation: $14x + 7 = 10x + 5$
Solve:
$14x - 10x = 5 - 7$
$4x = -2$
$x = \frac{-2}{4} = -\frac{1}{2}$

Answer:

Top Section (∠1 & ∠2):

7.) Relationship: Alternate Exterior Angles; Congruent
8.) Relationship: Alternate Interior Angles; Congruent
9.) Relationship: Corresponding Angles; Congruent

Middle Section (∠y & ∠x):

10.) Relationship: Alternate Interior Angles; Congruent
11.) Relationship: Same-Side Interior Angles; Supplementary
12.) Relationship: Corresponding Angles; Congruent

Bottom Section 1 (Solve for x):

13.) Relationship: Corresponding Angles; Congruent; Equation: $8x - 4 = 60$; $x = 8$
11.) (duplicate) Relationship: Same-Side Interior Angles; Supplementary; Equation: $(2x+43)+(2x-3)=180$; $x = 35$
12.) (duplicate) Relationship: Corresponding Angles; Congruent; Equation: $11x-2=75$; $x = 7$

Bottom Section 2 (Solve for x):

11.) (duplicate) Relationship: Same-Side Interior Angles; Supplementary; Equation: $(x+139)+132=180$; $x = -91$
12.) (duplicate) Relationship: Corresponding/Vertical Angles; Congruent; Equation: $2x+60=4x$; $x = 30$
13.) (duplicate) Relationship: Alternate Interior Angles; Congruent; Equation: $14x+7=10x+5$; $x = -\frac{1}{2}$