Triangle Test

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2. Two angles of a triangle are 40 degrees and 80 degrees. What is the measure of the third angle of the triangle?

80

60

120

30

Cannot be determined

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.

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.

3. Find the missing angle of the triangle below.

110

70

35

75

50

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.

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.

4. Describe a triangle with the following angle measures:
Angle A = 45 degrees, Angle B = 45 degrees, Angle C = 90 degrees.

Isosceles, Right Triangle

Scalene, Right Triangle

Equilateral, Right Triangle

Isosceles, Obtuse Triangle

Scalene, Acute Triangle

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."

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."

5. In Peter's daycare class there are 9 girls and 6 boys. What is the ratio of girls to boys in lowest terms?

2/3

2/5

3/2

3/5

2/1

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.

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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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?

3 inches

50 inches

100 inches

1 inch

Cannot be determined

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.

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.

8. 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?

6,750

30

465

435

Cannot be determined

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.

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.

9. 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?

3 feet

6 feet

5 feet

5.5 feet

Cannot be determined

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.

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.

10. 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.

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.

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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12. One base angle of an isosceles triangle is 40 degrees. Find the measure of the vertex angle. Use the diagram below to help you.

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.

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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13. If the tax rate is 10%, how much tax would you have to pay on a shirt that costs $28?

0.28

2.80

5.60

280

Cannot be determined

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.

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.

14. Given the pair of similar triangles below, find the missing side.

1. Identify Corresponding Sides

Since the triangles are similar, their corresponding sides are proportional. This means:

AB corresponds to DE

BC corresponds to EF

AC corresponds to DF

2. Set up a Proportion

We can use any pair of corresponding sides to set up a proportion. Let's use AB and DE, along with BC and EF:

AB/DE = BC/EF

3. Substitute the Known Values

We know AB = 15, DE = 6, and EF = 4. Substitute these values into the proportion:

15/6 = BC/4

4. Solve for BC

Cross-multiply: 15 * 4 = 6 * BC

Simplify: 60 = 6 * BC

Divide both sides by 6: BC = 10

Explanation

1. Identify Corresponding Sides

Since the triangles are similar, their corresponding sides are proportional. This means:

AB corresponds to DE

BC corresponds to EF

AC corresponds to DF

2. Set up a Proportion

We can use any pair of corresponding sides to set up a proportion. Let's use AB and DE, along with BC and EF:

AB/DE = BC/EF

3. Substitute the Known Values

We know AB = 15, DE = 6, and EF = 4. Substitute these values into the proportion:

15/6 = BC/4

4. Solve for BC

Cross-multiply: 15 * 4 = 6 * BC

Simplify: 60 = 6 * BC

Divide both sides by 6: BC = 10

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16. Three out of every five students take the CTA to school. Of 280 students, how many take the CTA?

56

118

285

168

Cannot be determined

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.

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.

17. In Peter's daycare class there are 9 girls and 6 boys. What is the ratio of girls to total students in lowest terms?

2/3

2/5

3/2

3/5

2/1

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.

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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19. Solve for the missing side of the following similar triangles. Round your answer to the nearest tenths place.

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.

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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