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ACT Exam  >  ACT Questions  >  In ΔABC below, points B, D, and C are c... Start Learning for Free
In ΔABC below, points B, D, and C are collinear. Segment AB is perpendicular to segment BC, and segment AD bisects angle BAC. If the measure of angle DCA is 60°, what is the measure of angle ADB?
  • a)
    15°
  • b)
    45°
  • c)
    60°
  • d)
    75°
  • e)
    105°
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In ΔABC below, points B, D, and C are collinear. Segment AB is p...
If the measure of angle DCA is 60°, then the measure of angle BCA is 60° as well. Because the angles in a triangle have the sum of 180°, angle BAC is 180 - 90 - 60, or 30°. Because the segment AD bisects angle BAC, angle BAD is equivalent to angle DAC, which is 30°/2, or 15°. Further, since the triangle ABD is a right triangle, the measure of angle ADB = 180 - 90 - 15, or 75°.
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Directions:Read the passages and choose the best answer to each question.PassageSOCIAL SCIENCE: Defining the Poverty Line: A Political QuestionPoverty is an enduring problem that must beaddressed by all modern societies. In fact, some ethi-cists say a civilization can be judged by how well ittreats its least fortunate. By this measure, the United(5) States has much to be proud of. On a national level, theUnited States has done remarkable work to decrease thesuffering of the poor by subsidizing food, housing, andeducation, and even by giving money directly to thosewho need it the most. Still, even in the public sector,(10) projects have to be evaluated to see if they are effec-tive. No one can measure the benefits of aid withoutdefining what poverty is, and when someone has beenlifted out of it. This leads to one very political question:How exactly should poverty be measured?(15) The question of poverty is extremely complex.Should it be considered absolute—as a simple mat-ter of the availability of food and shelter—or shouldit be relative to the goods and services enjoyed by thesociety as a whole? In other words, if a person can(20) afford a DVD player but not to live in a safe neighbor-hood, is that person poor? Certainly something as fluidas the economy can affect any number of forces tocause financial suffering—sometimes quite suddenly.Still, according to our federal government, there is(25) a specific measure, the “poverty line,” that answersthe question. Such a measure was devised in 1963 bygovernment economist Mollie Orshansky, then work-ing for the Social Security Administration under thejurisdiction of the Office of Management and Budget.(30) Orshansky’s statistical measurement was onesmall part of the federal government’s plan to attack thedifficult national economic conditions that were hurt-ing millions of Americans in the early 1960s. PresidentLyndon Johnson labeled the plan the government’s(35) “War on Poverty,” and it led to such national programsas Head Start, VISTA, and the Jobs Corps. Orshanskydeveloped her poverty threshold from a Departmentof Agriculture study outlining the cost of nutritionallyadequate meals.(40) From the Agriculture study, Orshansky took themost economic and healthy meal design she couldfind. She then estimated statistically that the averageAmerican family in the 1950s spent approximately one-third of its household income on food; from there, she(45) multiplied by three the cost of the most economicallyefficient, nutritional diet. This multiplier effect, in the-ory, produced the level of pre-tax household incomeat or below which a family should be considered poor.Orshansky’s calculation was distributed for use across(50) the government, and the measure came to be knownas the poverty line. It has been scaled every year forinflation, and it is adjustable to household size.Given the decades-old origins of this measure andthe limited data available to Orshansky at the time, it is(55) fair to wonder if her standard is still accurate. Studiesshow that it is not. While families today spend about12 percent of their income on food—nowhere near the33 percent assumed in the 1950s—the cost of importantbudget items, such as housing, transportation, and(60) health care, has increased dramatically. Orshansky’spoverty measure, which only takes into account theability of a household to provide itself with food, ismissing several essential components to be accuratein modern society. With over $60 billion in federal aid(65) tied each year to this guideline, not to mention an addi-tional $260 billion in Medicaid spending, the fact ismany Americans are still falling deeper into povertyand failing to receive the aid they so desperately needand deserve.(70) If reform of the measure of poverty used by soci-ety is an obvious need, it remains to be seen why suchreform has not been forthcoming. The answer lies inthe very politics that caused the measure to be createdin the first place. Any change in the measured poverty(75) level of a society is an indicator of economic healthwithin that society, and no president has been willingto increase the perceived amount of poverty for a sta-tistical recalculation, no matter how justified. Indeed,some economists say that updating the poverty measure(80) would increase the number of those considered poor,and therefore eligible for government aid, by as muchas 2 percentage points. That may not seem significant,but in real terms it means an additional several millionpeople are living below the “poverty line”—whether(85) we count them or not.Q.The main point of the first paragraph is that

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Directions:Read the passages and choose the best answer to each question.PassageSOCIAL SCIENCE: Defining the Poverty Line: A Political QuestionPoverty is an enduring problem that must beaddressed by all modern societies. In fact, some ethi-cists say a civilization can be judged by how well ittreats its least fortunate. By this measure, the United(5) States has much to be proud of. On a national level, theUnited States has done remarkable work to decrease thesuffering of the poor by subsidizing food, housing, andeducation, and even by giving money directly to thosewho need it the most. Still, even in the public sector,(10) projects have to be evaluated to see if they are effec-tive. No one can measure the benefits of aid withoutdefining what poverty is, and when someone has beenlifted out of it. This leads to one very political question:How exactly should poverty be measured?(15) The question of poverty is extremely complex.Should it be considered absolute—as a simple mat-ter of the availability of food and shelter—or shouldit be relative to the goods and services enjoyed by thesociety as a whole? In other words, if a person can(20) afford a DVD player but not to live in a safe neighbor-hood, is that person poor? Certainly something as fluidas the economy can affect any number of forces tocause financial suffering—sometimes quite suddenly.Still, according to our federal government, there is(25) a specific measure, the “poverty line,” that answersthe question. Such a measure was devised in 1963 bygovernment economist Mollie Orshansky, then work-ing for the Social Security Administration under thejurisdiction of the Office of Management and Budget.(30) Orshansky’s statistical measurement was onesmall part of the federal government’s plan to attack thedifficult national economic conditions that were hurt-ing millions of Americans in the early 1960s. PresidentLyndon Johnson labeled the plan the government’s(35) “War on Poverty,” and it led to such national programsas Head Start, VISTA, and the Jobs Corps. Orshanskydeveloped her poverty threshold from a Departmentof Agriculture study outlining the cost of nutritionallyadequate meals.(40) From the Agriculture study, Orshansky took themost economic and healthy meal design she couldfind. She then estimated statistically that the averageAmerican family in the 1950s spent approximately one-third of its household income on food; from there, she(45) multiplied by three the cost of the most economicallyefficient, nutritional diet. This multiplier effect, in the-ory, produced the level of pre-tax household incomeat or below which a family should be considered poor.Orshansky’s calculation was distributed for use across(50) the government, and the measure came to be knownas the poverty line. It has been scaled every year forinflation, and it is adjustable to household size.Given the decades-old origins of this measure andthe limited data available to Orshansky at the time, it is(55) fair to wonder if her standard is still accurate. Studiesshow that it is not. While families today spend about12 percent of their income on food—nowhere near the33 percent assumed in the 1950s—the cost of importantbudget items, such as housing, transportation, and(60) health care, has increased dramatically. Orshansky’spoverty measure, which only takes into account theability of a household to provide itself with food, ismissing several essential components to be accuratein modern society. With over $60 billion in federal aid(65) tied each year to this guideline, not to mention an addi-tional $260 billion in Medicaid spending, the fact ismany Americans are still falling deeper into povertyand failing to receive the aid they so desperately needand deserve.(70) If reform of the measure of poverty used by soci-ety is an obvious need, it remains to be seen why suchreform has not been forthcoming. The answer lies inthe very politics that caused the measure to be createdin the first place. Any change in the measured poverty(75) level of a society is an indicator of economic healthwithin that society, and no president has been willingto increase the perceived amount of poverty for a sta-tistical recalculation, no matter how justified. Indeed,some economists say that updating the poverty measure(80) would increase the number of those considered poor,and therefore eligible for government aid, by as muchas 2 percentage points. That may not seem significant,but in real terms it means an additional several millionpeople are living below the “poverty line”—whether(85) we count them or not.Q.The passage implies that no president has been willing to change the poverty measure for all of the following reasons EXCEPT

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In ΔABC below, points B, D, and C are collinear. Segment AB is perpendicular to segment BC, and segment AD bisects angle BAC. If the measure of angle DCA is 60°, what is the measure of angle ADB?a)15°b)45°c)60°d)75°e)105°Correct answer is option 'D'. Can you explain this answer?
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In ΔABC below, points B, D, and C are collinear. Segment AB is perpendicular to segment BC, and segment AD bisects angle BAC. If the measure of angle DCA is 60°, what is the measure of angle ADB?a)15°b)45°c)60°d)75°e)105°Correct answer is option 'D'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about In ΔABC below, points B, D, and C are collinear. Segment AB is perpendicular to segment BC, and segment AD bisects angle BAC. If the measure of angle DCA is 60°, what is the measure of angle ADB?a)15°b)45°c)60°d)75°e)105°Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In ΔABC below, points B, D, and C are collinear. Segment AB is perpendicular to segment BC, and segment AD bisects angle BAC. If the measure of angle DCA is 60°, what is the measure of angle ADB?a)15°b)45°c)60°d)75°e)105°Correct answer is option 'D'. Can you explain this answer?.
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