question 10 of 25

what is the measure of $\angle dfh$?

a. $47^\circ$
b. $53^\circ$
c. $86^\circ$
d. $43^\circ$

Question

question 10 of 25

what is the measure of $\angle dfh$?

a. $47^\circ$
b. $53^\circ$
c. $86^\circ$
d. $43^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circle Theorems" ], "new_concepts": [ "Secant-Secant Angle Theorem" ], "current_concepts": [ "Circle Theorems", "Secant-Secant Angle Theorem" ] } ## Identify the given arc measures and target angle $$ \begin{aligned} &m\widehat{DH} = 133^\circ\ &m\widehat{EG} = 47^\circ\ &\text{Target: } m\angle DFH \end{aligned} $$ ## Apply the Intersecting Secants Theorem $$ \begin{aligned} m\angle DFH &= \frac{1}{2}(m\widehat{DH} - m\widehat{EG})\ m\angle DFH &= \frac{1}{2}(133^\circ - 47^\circ) \end{aligned} $$ ## Calculate the final angle measure $$ \begin{aligned} m\angle DFH &= \frac{1}{2}(86^\circ) = 43^\circ \end{aligned} $$

A. $47^\circ$

B. $53^\circ$

C. $86^\circ$

D. $43^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given arc measures and target angle

Apply the Intersecting Secants Theorem

Calculate the final angle measure

Answer: