angle g is a circumscribed angle of circle e

what is the measure of angle g, in terms of x?

$x^\circ + x^\circ$
$x^\circ + 90^\circ$
$180^\circ - x^\circ$
$180^\circ - 2x^\circ$

Question

angle g is a circumscribed angle of circle e

what is the measure of angle g, in terms of x?

$x^\circ + x^\circ$
$x^\circ + 90^\circ$
$180^\circ - x^\circ$
$180^\circ - 2x^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circumscribed Angle Theorem" ], "new_concepts": [], "current_concepts": [ "Circumscribed Angle Theorem", "Circle Geometry" ] } ## Relate the central angle and the circumscribed angle $$ m\angle G + m\angle FED = 180^\circ $$ ## Find the central angle in terms of $x$ $$ \begin{aligned} &EF = ED \implies \triangle FED \text{ is isosceles}\ &m\angle EFD = m\angle EDF = x^\circ\ &m\angle FED = 180^\circ - 2x^\circ \end{aligned} $$ ## Solve for the measure of angle G $$ \begin{aligned} &m\angle G = 180^\circ - m\angle FED\ &m\angle G = 180^\circ - (180^\circ - 2x^\circ) = 2x^\circ \end{aligned} $$

(A) $x^\circ + x^\circ$

(B) $x^\circ + 90^\circ$

(C) $180^\circ - x^\circ$

(D) $180^\circ - 2x^\circ$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circumscribed Angle Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Relate the central angle and the circumscribed angle

Find the central angle in terms of \(x\)

Solve for the measure of angle G

Answer:

Relate the central angle and the circumscribed angle

Find the central angle in terms of \(x\)

Solve for the measure of angle G