question 10 of 10

in the diagram below, $\odot o$ is circumscribed about quadrilateral $defg$. what is the value of $x$?

a. 110
b. 70
c. 130
d. 80

Question

question 10 of 10

in the diagram below, $\odot o$ is circumscribed about quadrilateral $defg$. what is the value of $x$?

a. 110
b. 70
c. 130
d. 80

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inscribed Quadrilateral Theorem" ], "new_concepts": [], "current_concepts": [ "Inscribed Quadrilateral Theorem", "Circle Theorems" ] } ## Identify the relationship between opposite angles $$ \angle D + \angle F = 180^\circ \quad \text{and} \quad \angle E + \angle G = 180^\circ $$ ## Set up the equation for x $$ (x - 10) + 120 = 180 $$ ## Solve for x $$ \begin{aligned} x + 110 &= 180 \ x &= 70 \end{aligned} $$

A. 110

B. 70

C. 130

D. 80

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Inscribed Quadrilateral Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the relationship between opposite angles

Set up the equation for x

Solve for x

Answer: