what is the sum of the measures of the interior angles of $ghef$?

find $m \angle e$

Question

what is the sum of the measures of the interior angles of $ghef$?

find $m \angle e$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polygon Angle Sum Theorem", "Interior Angles of a Polygon" ], "new_concepts": [], "current_concepts": [ "Polygon Angle Sum Theorem", "Interior Angles of a Polygon" ] } ## Calculate the sum of the interior angles of quadrilateral GHEF $$ \begin{aligned} n &= 4 \ S &= (n - 2) \times 180^\circ \ S &= (4 - 2) \times 180^\circ = 360^\circ \end{aligned} $$ ## Solve for the measure of angle E $$ \begin{aligned} m\angle G + m\angle H + m\angle E + m\angle F &= 360^\circ \ 72^\circ + 83^\circ + m\angle E + 115^\circ &= 360^\circ \ 270^\circ + m\angle E &= 360^\circ \ m\angle E &= 90^\circ \end{aligned} $$ ## Question 1 What is the sum of the measures of the interior angles of $GHEF$? 360$^\circ$ ## Question 2 Find $m\angle E$ 90$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Polygon Angle Sum Theorem" ] }

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Question

Explanation:

Calculate the sum of the interior angles of quadrilateral GHEF

Solve for the measure of angle E

Answer:

Question 1

Question 2