g.gsr.8.1 (mc)
$\angle acb$ is a secant angle of circle f. $m\widehat{ab} = 170^\circ$ and $m\widehat{de} = 40^\circ$. find the measure of $\angle acb$.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Secant Angle" ], "new_concepts": [], "current_concepts": [ "Secant Angle", "Arc Measure" ] } ## State the formula for an angle formed by two secants intersecting outside a circle $$ m\angle ACB = \frac{1}{2}(m\widehat{AB} - m\widehat{DE}) $$ ## Substitute the given arc measures into the formula $$ \begin{aligned} m\widehat{AB} &= 170^\circ \ m\widehat{DE} &= 40^\circ \ m\angle ACB &= \frac{1}{2}(170^\circ - 40^\circ) \end{aligned} $$ ## Calculate the final angle measure $$ \begin{aligned} m\angle ACB &= \frac{1}{2}(130^\circ) \ m\angle ACB &= 65^\circ \end{aligned} $$ $65^\circ$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Secant Angle" ] }

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Question

Explanation:

State the formula for an angle formed by two secants intersecting outside a circle

Substitute the given arc measures into the formula

Calculate the final angle measure

Answer: