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

$m\angle mnl =$
$m\angle ink =$
$m\angle jnl =$

Question

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

$m\angle mnl =$
$m\angle ink =$
$m\angle jnl =$

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Vertical Angles", "Linear Pair" ], "new_concepts": [], "current_concepts": [ "Vertical Angles", "Linear Pair" ] } ## Identify vertical angle relationship $$ \begin{aligned} &\text{Lines } IL \text{ and } JM \text{ intersect at point } N.\ &m\angle MNL = m\angle JNI = 63^\circ \end{aligned} $$ ## Calculate linear pair angle $$ \begin{aligned} &m\angle JNK + m\angle KNL + m\angle MNL = 180^\circ\ &\text{From the diagram, } NK \text{ is perpendicular to } JM \text{ or } IL \text{ is a straight line.}\ &\text{Specifically, } IL \text{ is a straight line, so } m\angle JNI + m\angle JNK + m\angle KNL = 180^\circ.\ &\text{The diagram shows } \angle JNK \text{ and } \angle KNL \text{ are adjacent on the straight line } IL \text{ with } \angle JNI.\ &m\angle JNK = 90^\circ - m\angle JNI = 90^\circ - 63^\circ = 27^\circ \end{aligned} $$ ## Calculate remaining angle $$ \begin{aligned} &m\angle JNK + m\angle KNL = 180^\circ - m\angle JNI = 117^\circ\ &m\angle JNK = 27^\circ\ &m\angle KNL = 90^\circ\ &m\angle JNL = 180^\circ - m\angle JNI = 180^\circ - 63^\circ = 117^\circ \end{aligned} $$ ## Question 1 If $m\angle JNI = 63^\circ$, then $m\angle MNL =$ 63$^\circ$. ## Question 2 $m\angle JNK =$ 27$^\circ$ ## Question 3 $m\angle JNL =$ 117$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Vertical Angles" ] }

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QUESTION IMAGE

Question

Explanation:

Identify vertical angle relationship

Calculate linear pair angle

Calculate remaining angle

Answer:

Question 1

Question 2

Question 3