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Questions and Answers
1.
Two angles of a triangle are 40 degrees and 80 degrees. What is the measure of the third angle of the triangle?
A.
80
B.
60
C.
120
D.
30
E.
Cannot be determined
Correct Answer
B. 60
Explanation The sum of the angles in a triangle is always 180 degrees. Given that two angles of the triangle are 40 degrees and 80 degrees, we can find the measure of the third angle by subtracting the sum of the given angles from 180. Therefore, the measure of the third angle is 180 - (40 + 80) = 60 degrees.
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2.
Describe a triangle with the following angle measures:Angle A = 45 degrees, Angle B = 45 degrees, Angle C = 90 degrees.
A.
Isosceles, Right Triangle
B.
Scalene, Right Triangle
C.
Equilateral, Right Triangle
D.
Isosceles, Obtuse Triangle
E.
Scalene, Acute Triangle
Correct Answer
A. Isosceles, Right Triangle
Explanation The given triangle has two angles that are equal, which means it is an isosceles triangle. Additionally, one of the angles is 90 degrees, which classifies it as a right triangle. Therefore, the correct answer is "Isosceles, Right Triangle."
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3.
Find the missing angle of the triangle below.
A.
110
B.
70
C.
35
D.
75
E.
50
Correct Answer
B. 70
Explanation In a triangle, the sum of all angles is always 180 degrees. To find the missing angle, we can subtract the sum of the given angles from 180. In this case, the sum of the given angles (110 + 70 + 35) is 215. Subtracting 215 from 180 gives us -35. However, angles cannot be negative, so the missing angle must be 180 - 215 = 65 degrees.
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4.
In Peter's daycare class there are 9 girls and 6 boys. What is the ratio of girls to boys in lowest terms?
A.
2/3
B.
2/5
C.
3/2
D.
3/5
E.
2/1
Correct Answer
C. 3/2
Explanation The ratio of girls to boys in Peter's daycare class is 9:6, which can be simplified to 3:2. This means that for every 3 girls, there are 2 boys in the class.
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5.
In Peter's daycare class there are 9 girls and 6 boys. What is the ratio of girls to total students in lowest terms?
A.
2/3
B.
2/5
C.
3/2
D.
3/5
E.
2/1
Correct Answer
D. 3/5
Explanation The ratio of girls to total students can be found by dividing the number of girls by the total number of students. In this case, there are 9 girls and 15 total students (9 girls + 6 boys). Simplifying the ratio by dividing both the numerator and denominator by the greatest common divisor, we get 3/5.
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6.
If the ratio of students to teachers at a particular high school is 15 to 1, how many teachers are at the school if there are 450 students?
A.
6,750
B.
30
C.
465
D.
435
E.
Cannot be determined
Correct Answer
B. 30
Explanation Given that the ratio of students to teachers at the high school is 15 to 1, we can determine the number of teachers by dividing the number of students by the ratio. Therefore, if there are 450 students, the number of teachers at the school would be 450 divided by 15, which equals 30.
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7.
The scale on a certain map is 1 inch to 25 miles. How many inches would the distance between two cities that are 75 miles apart be on the map?
A.
3 inches
B.
50 inches
C.
100 inches
D.
1 inch
E.
Cannot be determined
Correct Answer
A. 3 inches
Explanation The scale on the map is 1 inch to 25 miles. This means that for every inch on the map, the actual distance is 25 miles. If the distance between two cities is 75 miles, we can calculate how many inches it would be on the map by dividing 75 miles by 25 miles per inch. The result is 3 inches, so the distance between the two cities would be represented as 3 inches on the map.
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8.
If the tax rate is 10%, how much tax would you have to pay on a shirt that costs $28?
A.
0.28
B.
2.80
C.
5.60
D.
280
E.
Cannot be determined
Correct Answer
B. 2.80
Explanation The tax rate is given as 10%, which means that you would have to pay 10% of the cost of the shirt as tax. The cost of the shirt is $28, so 10% of $28 is $2.80. Therefore, the correct answer is 2.80.
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9.
Three out of every five students take the CTA to school. Of 280 students, how many take the CTA?
A.
56
B.
118
C.
285
D.
168
E.
Cannot be determined
Correct Answer
D. 168
Explanation Based on the information given, three out of every five students take the CTA to school. This means that the ratio of students taking the CTA to those not taking it is 3:2. Therefore, if we divide the total number of students (280) into five equal parts, each part would represent 56 students. Since three parts represent the students taking the CTA, we can multiply 56 by 3 to find that 168 students take the CTA.
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10.
At the same time of day, man casts a 12 foot shadow and a 4 foot tall boy casts an 8 foot shadow. How tall is the man?
A.
3 feet
B.
6 feet
C.
5 feet
D.
5.5 feet
E.
Cannot be determined
Correct Answer
B. 6 feet
Explanation The height of an object is directly proportional to the length of its shadow. In this case, the man's shadow is 12 feet long while the boy's shadow is 8 feet long. If the boy is 4 feet tall, we can set up a proportion to find the man's height. 4/8 = x/12. Solving for x, we get x = 6. Therefore, the man is 6 feet tall.
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11.
Given the pair of similar triangles below, find the missing side.
Correct Answer 10
Explanation Since the triangles are similar, their corresponding sides are proportional. In this case, the missing side is equal to the corresponding side in the other triangle, which is 10.
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12.
Solve the following proportion.
Correct Answer 14
13.
Solve the following proportion for x.
Correct Answer 12
14.
Solve the following proportion for x.
Correct Answer 2
15.
Solve for the missing side given the similar triangles below:
Correct Answer 12
16.
Solve for the missing side of the following similar triangles. Round your answer to the nearest tenths place.
Correct Answer 13 13.3 13.33 13.333 13.3333
Explanation The given answer options are all rounded to the nearest tenths place, which means they have been rounded to the nearest decimal place with one digit after the decimal point. The missing side of the similar triangles should also be rounded to the nearest tenths place to maintain consistency with the given answer options. Therefore, any of the answer options can be considered correct as they all represent the missing side rounded to the nearest tenths place.
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17.
Find the missing side given the pair of similar triangles below.
Correct Answer 21
18.
One base angle of an isosceles triangle is 40 degrees. Find the measure of the vertex angle. Use the diagram below to help you.
Correct Answer 100
Explanation In an isosceles triangle, the base angles are congruent. Since one of the base angles is given as 40 degrees, the other base angle must also be 40 degrees. The sum of the three angles in any triangle is always 180 degrees. Therefore, the measure of the vertex angle can be found by subtracting the sum of the base angles from 180 degrees. In this case, 40 + 40 = 80, so the vertex angle is 180 - 80 = 100 degrees.
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19.
The vertex angle of an isosceles triangle is equal to 20 degrees. Find the measure of each of the base angles. Use the diagram below to help you.
Correct Answer 80
Explanation In an isosceles triangle, the base angles are always equal. Since the vertex angle is 20 degrees, each base angle must also be 20 degrees. Therefore, the measure of each of the base angles is 20 degrees.
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20.
Find the length of AB given the isosceles triangle below.Hint: you need to find x first and then plug it back in.
Correct Answer 13
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