Question

guided example 3

if \\( m\angle inj = 63^{\circ} \\), find each angle measure.

\\( m\angle mnl = \\) \\( ^{\circ} \\)

\\( m\angle jnk = \\) \\( ^{\circ} \\)

\\( m\angle jnl = \\) \\( ^{\circ} \\)

Explanation:

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<reasoning>

Identify vertical angles

\[

$$\begin{aligned} &m\angle INJ = 63^\circ \\ &m\angle MNL = m\angle INJ = 63^\circ \end{aligned}$$

\]

Calculate adjacent angle using linear pair

\[

$$\begin{aligned} &m\angle JNK + m\angle INJ = 90^\circ \quad (\text{from perpendicular marking } \angle INK = 90^\circ) \\ &m\angle JNK = 90^\circ - 63^\circ = 27^\circ \end{aligned}$$

\]

Calculate supplementary angle

\[

$$\begin{aligned} &m\angle JNL + m\angle INJ = 180^\circ \\ &m\angle JNL = 180^\circ - 63^\circ = 117^\circ \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

\(m\angle MNL =\) <blank>63</blank>

Question 2

\(m\angle JNK =\) <blank>27</blank>

Question 3

\(m\angle JNL =\) <blank>117</blank>
</answer>

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Answer:

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],
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</pre_analysis>

<reasoning>

Identify vertical angles

\[

$$\begin{aligned} &m\angle INJ = 63^\circ \\ &m\angle MNL = m\angle INJ = 63^\circ \end{aligned}$$

\]

Calculate adjacent angle using linear pair

\[

$$\begin{aligned} &m\angle JNK + m\angle INJ = 90^\circ \quad (\text{from perpendicular marking } \angle INK = 90^\circ) \\ &m\angle JNK = 90^\circ - 63^\circ = 27^\circ \end{aligned}$$

\]

Calculate supplementary angle

\[

$$\begin{aligned} &m\angle JNL + m\angle INJ = 180^\circ \\ &m\angle JNL = 180^\circ - 63^\circ = 117^\circ \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

\(m\angle MNL =\) <blank>63</blank>

Question 2

\(m\angle JNK =\) <blank>27</blank>

Question 3

\(m\angle JNL =\) <blank>117</blank>
</answer>

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