which graph represents a proportional relationship between x and y?
50. in this figure, the measure of ∠aed is 152°.
what is the degree measure of ∠ced?
a 26°
b. 38°
c. 42°
d. 84°

Question

Accepted Answer

### First Question (Graph Proportional Relationship)
# Brief Explanations:
A proportional relationship between $x$ and $y$ follows $y=kx$ (a linear equation passing through the origin $(0,0)$, with a constant ratio $\frac{y}{x}=k$).
1.  First graph: Starts at $(1,1)$, not the origin, so not proportional.
2.  Second graph: Horizontal line ($y=3$), $\frac{y}{x}$ is not constant, not proportional.
3.  Third graph: Starts at $(0,10)$, not the origin, so not proportional.
4.  Fourth graph: Straight line passing through $(0,0)$, $\frac{y}{x}$ is constant, so it represents a proportional relationship.
# Answer:
The fourth graph (bottom-right, starting at the origin with a shallow positive slope)

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### Second Question (Angle Calculation)
# Explanation:
## Step1: Set up linear equation
$\angle AED$ is a straight angle supplement to the sum of the three smaller angles:
$$x + 2x + (x-16) + 152 = 360$$
## Step2: Simplify and solve for $x$
Combine like terms and isolate $x$:
$$4x + 136 = 360$$
$$4x = 360 - 136 = 224$$
$$x = \frac{224}{4} = 56$$
## Step3: Calculate $\angle CED$
Substitute $x=56$ into $(x-16)$:
$$\angle CED = 56 - 16$$
# Answer:
A. $26^\circ$
Wait, correction: Step3 calculation: $56-16=40$? No, recheck Step1: $\angle AED = 152^\circ$, so the sum of $\angle AEB + \angle BEC + \angle CED = 180 - 152 = 28$? No, correct setup: The angles around point E sum to $360^\circ$, so the three angles plus $\angle AED$ equal $360^\circ$:
$$x + 2x + (x-16) + 152 = 360$$
$$4x = 360 - 152 +16 = 224$$
$$x=56$$
$\angle CED = x-16 = 56-16=40$? No, the options have 42, 38, 26, 84. Correct setup: $\angle AED$ is $152^\circ$, so the adjacent angles form a linear pair? No, $\angle AED$ is the large angle, so $\angle AEB + \angle BEC + \angle CED = 152^\circ$:
$$x + 2x + (x-16) = 152$$
$$4x -16 =152$$
$$4x=168$$
$$x=42$$
Then $\angle CED = 42-16=26^\circ$
# Corrected Explanation:
## Step1: Set up angle sum equation
The three smaller angles sum to $\angle AED$:
$$x + 2x + (x-16) = 152$$
## Step2: Solve for $x$
Combine terms and isolate $x$:
$$4x - 16 = 152$$
$$4x = 152 + 16 = 168$$
$$x = \frac{168}{4} = 42$$
## Step3: Calculate $\angle CED$
Substitute $x=42$ into $(x-16)$:
$$\angle CED = 42 - 16$$
# Corrected Answer:
A. $26^\circ$

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QUESTION IMAGE

Question

Explanation:

First Question (Graph Proportional Relationship)

Step1: Set up linear equation

Step2: Simplify and solve for $x$

Step3: Calculate $\angle CED$

Answer:

Second Question (Angle Calculation)