question 1 of 10

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

a. 24
b. 105
c. 36
d. 96

Question

question 1 of 10

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

a. 24
b. 105
c. 36
d. 96

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": [ "Inscribed Quadrilateral Theorem" ], "current_concepts": [ "Circle Theorems", "Inscribed Quadrilateral Theorem" ] } ## Set up the equation using the Inscribed Quadrilateral Theorem $$ \angle A + \angle C = 180^\circ $$ ## Substitute the given angle measures $$ 72^\circ + 3x^\circ = 180^\circ $$ ## Solve for $x$ $$ \begin{aligned} 3x &= 180 - 72 \ 3x &= 108 \ x &= 36 \end{aligned} $$

A. 24

B. 105

C. 36

D. 96

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the equation using the Inscribed Quadrilateral Theorem

Substitute the given angle measures

Solve for \(x\)

Answer: