Math Practice Problems - Solving For Angles

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=0, Mode=proportions

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

1.	A triangle has three angles labeled x, y, and z. The ratio of x to y is 6:3. The ratio of y to z is 3:1. What is the value of each of the angles, x, y, and z?	x = y = z =
2.	A triangle has three angles labeled x, y, and z. The ratio of x to y is 10:23. The ratio of y to z is 23:3. What is the value of each of the angles, x, y, and z?	x = y = z =

Complexity=1, Mode=complementary

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

1.	A triangle has three angles labeled x, y, and z. x and y are complementary angles and the ratio of x to y is 21:9. What is the value of each of the angles, x, y, and z?	x = y = z =
2.	A triangle has three angles labeled x, y, and z. z and x are complementary angles and the ratio of z to x is 2:1. What is the value of each of the angles, x, y, and z?	x = y = z =

Complexity=2, Mode=supplementary

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

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 = 53 degrees, b = 7 degrees, and the ratio of x to y is 1:1. What is the value of c, x, y, and z?	c = x = y = z =
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 = 56 degrees, b = 19 degrees, and the ratio of x to y is 5:4. What is the value of c, x, y, and z?	c = x = y = z =

Complexity=3

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

1.	A triangle has three angles labeled x, y, and z. y and z are complementary angles and the ratio of y to z is 3:2. What is the value of each of the angles, x, y, and z?	x = y = z =
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 = 91 degrees, b = 65 degrees, and the ratio of x to y is 26:3. What is the value of c, x, y, and z?	c = x = y = z =

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 6:3. The ratio of y to z is 3:1. What is the value of each of the angles, x, y, and z?	x = y = z =
Solution Write ratios in terms of n: 6n + 3n + 1n = 180 degrees 10n = 180 degrees n = 180 ÷ 10 = 18 degrees x = 6 × n = 6 × 18 = 108 degrees y = 3 × n = 3 × 18 = 54 degrees z = 1 × n = 1 × 18 = 18 degrees

#	Problem	Correct Answer	Your Answer
2	A triangle has three angles labeled x, y, and z. The ratio of x to y is 10:23. The ratio of y to z is 23:3. What is the value of each of the angles, x, y, and z?	x = y = z =
Solution Write ratios in terms of n: 10n + 23n + 3n = 180 degrees 36n = 180 degrees n = 180 ÷ 36 = 5 degrees x = 10 × n = 10 × 5 = 50 degrees y = 23 × n = 23 × 5 = 115 degrees z = 3 × n = 3 × 5 = 15 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. x and y are complementary angles and the ratio of x to y is 21:9. 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: 21n + 9n = 90 degress 30n = 90 degrees n = 90 / 30 = 3 degrees x = 21 × n = 21 × 3 = 63 degrees y = 9 × n = 9 × 3 = 27 degrees z = 180 - (x + y) = 180 - 90 = 90 degrees

#	Problem	Correct Answer	Your Answer
2	A triangle has three angles labeled x, y, and z. z and x are complementary angles and the ratio of z to x is 2:1. 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 + 1n = 90 degress 3n = 90 degrees n = 90 / 3 = 30 degrees z = 2 × n = 2 × 30 = 60 degrees x = 1 × n = 1 × 30 = 30 degrees y = 180 - (z + x) = 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 = 53 degrees, b = 7 degrees, and the ratio of x to y is 1:1. What is the value of c, x, y, and z?	c = x = y = z =
Solution a + b + c = 180 degrees 53 + 7 + c = 180 degrees 60 + c = 180 degrees c = 120 degrees c and x supplementary: c + x = 180 degrees 120 + x = 180 degrees x = 60 degrees Ratio of x to y: x:y = 1:1 x ÷ y = 1 ÷ 1 y = x × 1 ÷ 1 = 60 × 1 ÷ 1 = 60 degrees x + y + z = 180 degrees 60 + 60 + z = 180 degrees 120 + z = 180 degrees z = 60 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 = 56 degrees, b = 19 degrees, and the ratio of x to y is 5:4. What is the value of c, x, y, and z?	c = x = y = z =
Solution a + b + c = 180 degrees 56 + 19 + c = 180 degrees 75 + c = 180 degrees c = 105 degrees c and x supplementary: c + x = 180 degrees 105 + x = 180 degrees x = 75 degrees Ratio of x to y: x:y = 5:4 x ÷ y = 5 ÷ 4 y = x × 4 ÷ 5 = 75 × 4 ÷ 5 = 60 degrees x + y + z = 180 degrees 75 + 60 + z = 180 degrees 135 + z = 180 degrees z = 45 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. y and z are complementary angles and the ratio of y to z is 3:2. What is the value of each of the angles, x, y, and z?	x = y = z =
Solution y and z complementary: y + z = 90 degrees Write y and z in terms of n for ratio: 3n + 2n = 90 degress 5n = 90 degrees n = 90 / 5 = 18 degrees y = 3 × n = 3 × 18 = 54 degrees z = 2 × n = 2 × 18 = 36 degrees x = 180 - (y + z) = 180 - 90 = 90 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 = 91 degrees, b = 65 degrees, and the ratio of x to y is 26:3. What is the value of c, x, y, and z?	c = x = y = z =
Solution a + b + c = 180 degrees 91 + 65 + c = 180 degrees 156 + c = 180 degrees c = 24 degrees c and x supplementary: c + x = 180 degrees 24 + x = 180 degrees x = 156 degrees Ratio of x to y: x:y = 26:3 x ÷ y = 26 ÷ 3 y = x × 3 ÷ 26 = 156 × 3 ÷ 26 = 18 degrees x + y + z = 180 degrees 156 + 18 + z = 180 degrees 174 + z = 180 degrees z = 6 degrees

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