question 4 of 10

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

a. $80^\circ$
b. $60^\circ$
c. $100^\circ$
d. $120^\circ$

Question

question 4 of 10

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

a. $80^\circ$
b. $60^\circ$
c. $100^\circ$
d. $120^\circ$

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 of an inscribed quadrilateral $$ \angle B + \angle D = 180^\circ $$ ## Substitute the given values and solve for x $$ \begin{aligned} 100^\circ + x^\circ &= 180^\circ \ x &= 80 \end{aligned} $$

A. 80°

B. 60°

C. 100°

D. 120°

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

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Question

Explanation:

Identify the relationship between opposite angles of an inscribed quadrilateral

Substitute the given values and solve for x

Answer: