Math Practice Problems - Solving For Angles

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Solving For Angles - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=1, Mode=complementary

Find the values of the following angles to the nearest degree.

Complexity=2, Mode=supplementary

Find the values of the following angles to the nearest degree.

Complexity=3

Find the values of the following angles to the nearest degree.

Answers

Complexity=0, Mode=proportions

Find the values of the following angles to the nearest degree.

#	Problem	Correct Answer	Your Answer
1	A triangle has three angles labeled x, y, and z. The ratio of x to y is 6:38. The ratio of y to z is 38:1. What is the value of each of the angles, x, y, and z?	x = y = z =
Solution Write ratios in terms of n: 6n + 38n + 1n = 180 degrees 45n = 180 degrees n = 180 ÷ 45 = 4 degrees x = 6 × n = 6 × 4 = 24 degrees y = 38 × n = 38 × 4 = 152 degrees z = 1 × n = 1 × 4 = 4 degrees

#	Problem	Correct Answer	Your Answer
2	A triangle has three angles labeled x, y, and z. The ratio of x to y is 3:1. The ratio of y to z is 1:2. What is the value of each of the angles, x, y, and z?	x = y = z =
Solution Write ratios in terms of n: 3n + 1n + 2n = 180 degrees 6n = 180 degrees n = 180 ÷ 6 = 30 degrees x = 3 × n = 3 × 30 = 90 degrees y = 1 × n = 1 × 30 = 30 degrees z = 2 × n = 2 × 30 = 60 degrees

Complexity=1, Mode=complementary

Find the values of the following angles to the nearest degree.

#	Problem	Correct Answer	Your Answer
1	A triangle has three angles labeled x, y, and z. z and x are complementary angles and the ratio of z to x is 2:7. What is the value of each of the angles, x, y, and z?	x = y = z =
Solution z and x complementary: z + x = 90 degrees Write z and x in terms of n for ratio: 2n + 7n = 90 degress 9n = 90 degrees n = 90 / 9 = 10 degrees z = 2 × n = 2 × 10 = 20 degrees x = 7 × n = 7 × 10 = 70 degrees y = 180 - (z + x) = 180 - 90 = 90 degrees

#	Problem	Correct Answer	Your Answer
2	A triangle has three angles labeled x, y, and z. x and y are complementary angles and the ratio of x to y is 14:16. What is the value of each of the angles, x, y, and z?	x = y = z =
Solution x and y complementary: x + y = 90 degrees Write x and y in terms of n for ratio: 14n + 16n = 90 degress 30n = 90 degrees n = 90 / 30 = 3 degrees x = 14 × n = 14 × 3 = 42 degrees y = 16 × n = 16 × 3 = 48 degrees z = 180 - (x + y) = 180 - 90 = 90 degrees

Complexity=2, Mode=supplementary

Find the values of the following angles to the nearest degree.

#	Problem	Correct Answer	Your Answer
1	Angles a, b, and c make up one triangle. Angles x, y, and z make up another triangle. Angles c and x are supplementary. Furthermore, a = 74 degrees, b = 16 degrees, and the ratio of x to y is 9:4. What is the value of c, x, y, and z?	c = x = y = z =
Solution a + b + c = 180 degrees 74 + 16 + c = 180 degrees 90 + c = 180 degrees c = 90 degrees c and x supplementary: c + x = 180 degrees 90 + x = 180 degrees x = 90 degrees Ratio of x to y: x:y = 9:4 x ÷ y = 9 ÷ 4 y = x × 4 ÷ 9 = 90 × 4 ÷ 9 = 40 degrees x + y + z = 180 degrees 90 + 40 + z = 180 degrees 130 + z = 180 degrees z = 50 degrees

#	Problem	Correct Answer	Your Answer
2	Angles a, b, and c make up one triangle. Angles x, y, and z make up another triangle. Angles c and x are supplementary. Furthermore, a = 17 degrees, b = 3 degrees, and the ratio of x to y is 2:6. What is the value of c, x, y, and z?	c = x = y = z =
Solution a + b + c = 180 degrees 17 + 3 + c = 180 degrees 20 + c = 180 degrees c = 160 degrees c and x supplementary: c + x = 180 degrees 160 + x = 180 degrees x = 20 degrees Ratio of x to y: x:y = 2:6 x ÷ y = 2 ÷ 6 y = x × 6 ÷ 2 = 20 × 6 ÷ 2 = 60 degrees x + y + z = 180 degrees 20 + 60 + z = 180 degrees 80 + z = 180 degrees z = 100 degrees

Complexity=3

Find the values of the following angles to the nearest degree.

#	Problem	Correct Answer	Your Answer
1	A triangle has three angles labeled x, y, and z. The ratio of x to y is 13:1. The ratio of y to z is 1:1. What is the value of each of the angles, x, y, and z?	x = y = z =
Solution Write ratios in terms of n: 13n + 1n + 1n = 180 degrees 15n = 180 degrees n = 180 ÷ 15 = 12 degrees x = 13 × n = 13 × 12 = 156 degrees y = 1 × n = 1 × 12 = 12 degrees z = 1 × n = 1 × 12 = 12 degrees

#	Problem	Correct Answer	Your Answer
2	A triangle has three angles labeled x, y, and z. The ratio of x to y is 4:6. The ratio of y to z is 6:2. What is the value of each of the angles, x, y, and z?	x = y = z =
Solution Write ratios in terms of n: 4n + 6n + 2n = 180 degrees 12n = 180 degrees n = 180 ÷ 12 = 15 degrees x = 4 × n = 4 × 15 = 60 degrees y = 6 × n = 6 × 15 = 90 degrees z = 2 × n = 2 × 15 = 30 degrees

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