find the measure of $\angle egc$. (1 point)

$140^\circ$
$90^\circ$
$70^\circ$
$50^\circ$

Question

find the measure of $\angle egc$. (1 point)

$140^\circ$
$90^\circ$
$70^\circ$
$50^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Circle Geometry" ], "new_concepts": [ "Angles of Intersecting Chords" ], "current_concepts": [ "Circle Geometry", "Angles of Intersecting Chords" ] } ## Relate angle to intercepted arcs Using the *Circle Geometry* knowledge point $$ m\angle EGC = \frac{m\overparen{CE} + m\overparen{DF}}{2} $$ ## Set up the equation for x Using the *Circle Geometry* knowledge point $$ \begin{aligned} 7x + 7 &= \frac{50 + 10x}{2} \ 7x + 7 &= 25 + 5x \end{aligned} $$ ## Solve for x Using the *Circle Geometry* knowledge point $$ \begin{aligned} 2x &= 18 \ x &= 9 \end{aligned} $$ ## Calculate the measure of angle EGC Using the *Circle Geometry* knowledge point $$ \begin{aligned} m\angle EGC &= 7(9) + 7 \ m\angle EGC &= 63 + 7 = 70^\circ \end{aligned} $$

(A) $140^\circ$

(B) $90^\circ$

(C) $70^\circ$

(D) $50^\circ$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Angles of Intersecting Chords" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Relate angle to intercepted arcs

Set up the equation for x

Solve for x

Calculate the measure of angle EGC

Answer: