if abcd is a rectangle, and (m\angle adb = 55^\circ), what is the value of (x)?

a. 80
b. 90
c. 40
d. 70
e. 110
f. cannot be determined

Question

if abcd is a rectangle, and (m\angle adb = 55^\circ), what is the value of (x)?

a. 80
b. 90
c. 40
d. 70
e. 110
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 $$ \begin{aligned} &AC = BD\ &AE = EC = \frac{1}{2}AC\ &DE = EB = \frac{1}{2}BD\ &DE = AE \end{aligned} $$ ## Determine base angles of the isosceles triangle Using the *Isosceles Triangle Theorem* knowledge point $$ \begin{aligned} &\triangle ADE \text{ is isosceles with } DE = AE\ &m\angle DAE = m\angle ADE = 55^\circ \end{aligned} $$ ## Calculate the vertex angle Using the *Triangle Angle Sum Theorem* knowledge point $$ \begin{aligned} &m\angle AED + m\angle DAE + m\angle ADE = 180^\circ\ &m\angle AED + 55^\circ + 55^\circ = 180^\circ\ &m\angle AED = 70^\circ \end{aligned} $$ ## Find the value of x Using the *Properties of Rectangles* knowledge point $$ \begin{aligned} &x^\circ \text{ and } m\angle AED \text{ are vertical angles}\ &x = m\angle AED = 70 \end{aligned} $$

A. 80

B. 90

C. 40

D. 70

E. 110

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 base angles of the isosceles triangle

Calculate the vertex angle

Find the value of x

Answer: