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## Angle Measurements 2 - 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=vert

Solve for the missing angle(s).
Figures are not drawn to scale.

1.   In the figure below, two lines intersect to form ∠A,
B, ∠C, and ∠D. If m∠A = 52°, find the missing angles.
m∠B = °
m∠C = °
m∠D = °
2.   In the figure below, two lines intersect to form ∠A,
B, ∠C, and ∠D. If m∠C = 89°, find the missing angles.
m∠A = °
m∠B = °
m∠D = °

### Complexity=1, Mode=tran

Solve for the missing angle(s).
Figures are not drawn to scale.

1.   In the figure below, lines g and h are parallel, and line m is a transversal. If m∠8 = 94°, what is m∠3?      °
2.   In the figure below, lines g and h are parallel, and line m is a transversal. If m∠1 = 107°, what is m∠6?      °

### Complexity=1, Mode=round

Solve for the missing angle(s).
Figures are not drawn to scale.

1.   If m∠B + m∠D = 175° and m∠C = 40°, what is m∠A?   °
2.   If m∠A + m∠B + m∠C = 230° and m∠E = 70°, what is m∠D?   °

### Complexity=1

Solve for the missing angle(s).
Figures are not drawn to scale.

1.   In the figure below, three lines intersect to form a triangle with interior angles W, F, and D. If m∠W = 70° and m∠F = 70°, what is m∠C?   °
2.   In the figure below, lines g and h are parallel, and line m is a transversal. If m∠4 = 82°, find the missing angles.
m∠5 = °
m∠6 = °
m∠8 = °

### Complexity=1, Mode=vert

Solve for the missing angle(s).
Figures are not drawn to scale.

1In the figure below, two lines intersect to form ∠A,
B, ∠C, and ∠D. If m∠A = 52°, find the missing angles.

m∠B = °
m∠C = °
m∠D = °
Solution

A and ∠B are supplementary angles which means they add up to 180°.
 m∠A + m∠B = 180° m∠B = 180° - m∠A m∠B = 180° - 52° = 128°

A and ∠C are vertical angles which means they are equal.
m∠A = m∠C = 52°

A and ∠D are supplementary angles which means they add up to 180°.
 m∠A + m∠D = 180° m∠D = 180° - m∠A m∠D = 180° - 52° = 128°

2In the figure below, two lines intersect to form ∠A,
B, ∠C, and ∠D. If m∠C = 89°, find the missing angles.

m∠A = °
m∠B = °
m∠D = °
Solution

C and ∠A are vertical angles which means they are equal.
m∠C = m∠A = 89°

C and ∠B are supplementary angles which means they add up to 180°.
 m∠C + m∠B = 180° m∠B = 180° - m∠C m∠B = 180° - 89° = 91°

C and ∠D are supplementary angles which means they add up to 180°.
 m∠C + m∠D = 180° m∠D = 180° - m∠C m∠D = 180° - 89° = 91°

### Complexity=1, Mode=tran

Solve for the missing angle(s).
Figures are not drawn to scale.

1In the figure below, lines g and h are parallel, and line m is a transversal. If m∠8 = 94°, what is m∠3?      °
Solution
One property of the angles created by the transversal that cuts across two parallel lines is
m∠8 = m∠4
∠4 and ∠3 are supplementary angles.
m∠4 + m∠3 = 180°
Substituting m∠8 for m∠4 in the second equation, we get
 m∠8 + m∠3 = 180° 94° + m∠3 = 180° m∠3 = 180° - 94° = 86°
2In the figure below, lines g and h are parallel, and line m is a transversal. If m∠1 = 107°, what is m∠6?      °
Solution
One property of the angles created by the transversal that cuts across two parallel lines is
m∠1 = m∠5
∠5 and ∠6 are supplementary angles.
m∠5 + m∠6 = 180°
Substituting m∠1 for m∠5 in the second equation, we get
 m∠1 + m∠6 = 180° 107° + m∠6 = 180° m∠6 = 180° - 107° = 73°

### Complexity=1, Mode=round

Solve for the missing angle(s).
Figures are not drawn to scale.

1 If m∠B + m∠D = 175° and m∠C = 40°, what is m∠A?   °
Solution
The sum of angles around a point is 360°.
 m∠A + m∠B + m∠C + m∠D = 360° m∠A + (m∠B + m∠D) + m∠C = 360° m∠A + 175° + 40° = 360° 215° + m∠A = 360° m∠A = 360° - 215° = 145°
2 If m∠A + m∠B + m∠C = 230° and m∠E = 70°, what is m∠D?   °
Solution
The sum of angles around a point is 360°.
 m∠A + m∠B + m∠C + m∠D + m∠E = 360° (m∠A + m∠B + m∠C) + m∠D + m∠E = 360° 230° + m∠D + 70° = 360° 300° + m∠D = 360° m∠D = 360° - 300° = 60°

### Complexity=1

Solve for the missing angle(s).
Figures are not drawn to scale.

1In the figure below, three lines intersect to form a triangle with interior angles W, F, and D. If m∠W = 70° and m∠F = 70°, what is m∠C?   °
Solution
The three angles in the triangle add up to 180°.
m∠W + m∠F + m∠D = 180°
∠D and ∠C are supplementary angles.
m∠D + m∠C = 180°
Set the two equations as equal.
 m∠W + m∠F + m∠D = m∠D + m∠C m∠W + m∠F = m∠C 70° + 70° = m∠C 140° = m∠C