Question

multiple choice
find the value of (x).

image showing a straight line ad with a ray bc originating from point b. the angle abc is labeled ((x + 25)^circ) and the angle cbd is labeled ((4x - 10)^circ).

a (x = 160)
b (x = 58)
c (x = 122)
d (x = 33)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Linear Pair Postulate",
"Supplementary Angles",
"Linear Equations"
],
"new_concepts": [],
"current_concepts": [
"Linear Pair Postulate",
"Supplementary Angles",
"Linear Equations"
]
}
</pre_analysis>

<reasoning>

Set up the linear pair equation

\[
(x + 25) + (4x - 10) = 180
\]

Simplify and solve for x

\[

$$\begin{aligned} 5x + 15 &= 180 \\ 5x &= 165 \\ x &= 33 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(x = 160\)</mcq-option>
<mcq-option>(B) \(x = 58\)</mcq-option>
<mcq-option>(C) \(x = 122\)</mcq-option>
<mcq-correct>(D) \(x = 33\)</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Linear Pair Postulate"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Linear Pair Postulate",
"Supplementary Angles",
"Linear Equations"
],
"new_concepts": [],
"current_concepts": [
"Linear Pair Postulate",
"Supplementary Angles",
"Linear Equations"
]
}
</pre_analysis>

<reasoning>

Set up the linear pair equation

\[
(x + 25) + (4x - 10) = 180
\]

Simplify and solve for x

\[

$$\begin{aligned} 5x + 15 &= 180 \\ 5x &= 165 \\ x &= 33 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(x = 160\)</mcq-option>
<mcq-option>(B) \(x = 58\)</mcq-option>
<mcq-option>(C) \(x = 122\)</mcq-option>
<mcq-correct>(D) \(x = 33\)</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Linear Pair Postulate"
]
}
</post_analysis>