if (abcd) is a rectangle and (m\angle cbd = 47^\circ), what is the value of (x)?

a. 47
b. 133
c. 94
d. 86
e. 43
f. cannot be determined

Question

if (abcd) is a rectangle and (m\angle cbd = 47^\circ), what is the value of (x)?

a. 47
b. 133
c. 94
d. 86
e. 43
f. cannot be determined

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Properties of Rectangles", "Isosceles Triangle Theorem", "Triangle Angle Sum Theorem" ], "new_concepts": [], "current_concepts": [ "Properties of Rectangles", "Isosceles Triangle Theorem", "Triangle Angle Sum Theorem" ] } ## Identify properties of the diagonals Using the *Properties of Rectangles* knowledge point $$ \begin{aligned} &AC = BD\ &AO = OC = BO = OD\ &BO = CO \end{aligned} $$ ## Determine the angles of the isosceles triangle Using the *Isosceles Triangle Theorem* knowledge point $$ \begin{aligned} &\triangle BOC \text{ is isosceles with } BO = CO\ &m\angle OCB = m\angle OBC = 47^\circ \end{aligned} $$ ## Calculate the value of x Using the *Triangle Angle Sum Theorem* knowledge point $$ \begin{aligned} &m\angle BOC + m\angle OBC + m\angle OCB = 180^\circ\ &x + 47^\circ + 47^\circ = 180^\circ\ &x + 94^\circ = 180^\circ\ &x = 86^\circ \end{aligned} $$

A. 47

B. 133

C. 94

D. 86

E. 43

F. Cannot be determined

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Properties of Rectangles" ] }

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QUESTION IMAGE

Question

Explanation:

Identify properties of the diagonals

Determine the angles of the isosceles triangle

Calculate the value of x

Answer: