Question

what is \\(m\angle 1\\)?

\\(m\angle 1 = \boxed{\phantom{x}}^{\circ}\\)

Explanation:

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"Exterior Angle Theorem",
"Triangle Angle Sum"
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"Exterior Angle Theorem",
"Triangle Angle Sum"
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<reasoning>

Identify the given angles and the target angle

We are given a triangle with two known interior angles:

• One interior angle measures \(68^\circ\).
• Another interior angle measures \(37^\circ\).
• The target angle is \(\angle 1\), which is an exterior angle of the triangle.

Apply the Exterior Angle Theorem

The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
\[
m\angle 1 = 68^\circ + 37^\circ
\]

Calculate the final measure

Add the two interior angle measures together:
\[
m\angle 1 = 105^\circ
\]
</reasoning>

<answer>
What is \(m\angle 1\)?

\(m\angle 1 =\) <blank>105</blank>\(^\circ\)
</answer>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Exterior Angle Theorem"
]
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Answer:

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"Triangle Angle Sum"
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</pre_analysis>

<reasoning>

Identify the given angles and the target angle

We are given a triangle with two known interior angles:

• One interior angle measures \(68^\circ\).
• Another interior angle measures \(37^\circ\).
• The target angle is \(\angle 1\), which is an exterior angle of the triangle.

Apply the Exterior Angle Theorem

The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
\[
m\angle 1 = 68^\circ + 37^\circ
\]

Calculate the final measure

Add the two interior angle measures together:
\[
m\angle 1 = 105^\circ
\]
</reasoning>

<answer>
What is \(m\angle 1\)?

\(m\angle 1 =\) <blank>105</blank>\(^\circ\)
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Exterior Angle Theorem"
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