in circle y, what is \$m\\widehat{tu}\$? \$59^\\circ\$ \\(67^\\circ…

QUESTION IMAGE

$in circle y, what is \$m\\widehat{tu}\$? \$59^\\circ\$ \\(67^\\circ…$

Question

in circle y, what is \$m\widehat{tu}\$?

\$59^\circ\$
\$67^\circ\$
\$71^\circ\$
\$118^\circ\$

Explanation:

Response

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Angles of Intersecting Chords",
"Circle Arc Measure"
],
"new_concepts": [],
"current_concepts": [
"Angles of Intersecting Chords",
"Circle Arc Measure"
]
}
</pre_analysis>

Apply the intersecting chords theorem

\[
\theta = \frac{m\widehat{RS} + m\widehat{TU}}{2}
\]

Substitute the given values

\[
63^\circ = \frac{55^\circ + m\widehat{TU}}{2}
\]

Solve for the unknown arc measure

\[

\begin{aligned} 126^\circ &= 55^\circ + m\widehat{TU} \\ m\widehat{TU} &= 71^\circ \end{aligned}

\]
</reasoning>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Angles of Intersecting Chords"
]
}
</post_analysis>

Answer: