in the diagram below, $\overline{de}$ and $\overline{ef}$ are tangent to $\odot o$. what is the measure of $\widehat{dgf}$?

a. $207^\circ$
b. $252^\circ$
c. $180^\circ$
d. $126^\circ$

Question

in the diagram below, $\overline{de}$ and $\overline{ef}$ are tangent to $\odot o$. what is the measure of $\widehat{dgf}$?

a. $207^\circ$
b. $252^\circ$
c. $180^\circ$
d. $126^\circ$

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": [ "Arc Measure", "Major Arc", "Minor Arc" ], "new_concepts": [], "current_concepts": [ "Arc Measure", "Major Arc", "Minor Arc", "Tangent Line", "Angles Outside Circle Theorem" ] } ## Identify the given values Using the *Arc Measure* knowledge point $$ \begin{aligned} &m\widehat{DF} = 153^\circ\ &m\angle E = 27^\circ \end{aligned} $$ ## Define the relationship between the arcs Using the *Minor Arc* and *Major Arc* knowledge points $$ \begin{aligned} &m\widehat{DF} + m\widehat{DGF} = 360^\circ \end{aligned} $$ ## Calculate the measure of the major arc Using the *Arc Measure* knowledge point $$ \begin{aligned} &m\widehat{DGF} = 360^\circ - 153^\circ = 207^\circ \end{aligned} $$

(A) $207^\circ$

(B) $252^\circ$

(C) $180^\circ$

(D) $126^\circ$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Arc Measure" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values

Define the relationship between the arcs

Calculate the measure of the major arc

Answer: