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  3. Compare Quantity A and Quantity B, using additional information centered above t

Compare Quantity A and Quantity B, using additional information centered above t

游客2024-01-12  9
问题 Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:
(A)Quantity A is greater.
(B)Quantity B is greater.
(C)The two quantities are equal.
(D)The relationship cannot be determined from the information given.
A symbol that appears more than once in a question has the same meaning throughout the question. [br]
Quantity A   Quantity B
x             120
选项
答案 B
解析 Note that there are four angles in the figure: the three interior angles of triangle ABC and the exterior angle at vertex A. Since the measure of the exterior angle at vertex A is x degrees, it follows that the measure of interior angle A is(180 - x)°. Also, since AB = BC, it follows that triangle ABC is isosceles and the measures of interior angles A and C are equal. Therefore the measure of interior angle C is also(180 - x)°.
Since the sum of the measures of the interior angles of a triangle is 180° and you are given that the measure of interior angle B is 40°, it follows that
40 +(180 -x)+(180 -x)= 180.
Solving the equation for x gives x = 110. Since Quantity B is 120, the correct answer is Choice B.
This explanation uses the following strategies.
Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship
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