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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=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 6:38. 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 = 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 =

### 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. 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 = 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 =

### 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 = 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 = 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 =

### Complexity=3

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 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 = 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 =

### Complexity=0, Mode=proportions

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

1A 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
2A 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.

1A 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
2A 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.

1Angles 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
2Angles 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.

1A 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
2A 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