Angle Relationships Practice Worksheet

Practice complementary angles, supplementary angles, vertical angles, linear pairs, and parallel line angle rules.

Try each problem on your own first. Then click Show solution to check the angle relationship, equation setup, and final answer.

Angle Relationship Rules

  • Complementary angles: add to \(90^\circ\)
  • Supplementary angles: add to \(180^\circ\)
  • Vertical angles: are congruent
  • Linear pairs: are supplementary
  • Corresponding angles: are congruent when lines are parallel
  • Alternate interior angles: are congruent when lines are parallel
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Level 1: Complementary and Supplementary Angles

Problem 1

Two angles are complementary. One angle measures \(38^\circ\). Find the other angle.

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Complementary angles add to \(90^\circ\).

\[ 90^\circ - 38^\circ = 52^\circ \]

The other angle is \(52^\circ\).

Problem 2

Two angles are supplementary. One angle measures \(124^\circ\). Find the other angle.

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Supplementary angles add to \(180^\circ\).

\[ 180^\circ - 124^\circ = 56^\circ \]

The other angle is \(56^\circ\).

Problem 3

Two supplementary angles are \(x\) and \(2x\). Find both angle measures.

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Supplementary angles add to \(180^\circ\).

\[ x+2x=180 \] \[ 3x=180 \] \[ x=60 \]

So the two angles are:

\[ 60^\circ \quad \text{and} \quad 120^\circ \]

Level 2: Vertical Angles and Linear Pairs

Problem 4

Two vertical angles are labeled \(5x+10\) and \(80\). Find \(x\).

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Vertical angles are congruent, so set them equal.

\[ 5x+10=80 \] \[ 5x=70 \] \[ x=14 \]
Problem 5

Two angles form a linear pair. Their measures are \(3x\) and \(x+40\). Find \(x\).

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A linear pair is supplementary.

\[ 3x+(x+40)=180 \] \[ 4x+40=180 \] \[ 4x=140 \] \[ x=35 \]
Problem 6

Two adjacent angles form a straight line. One angle is \(72^\circ\). Find the other angle.

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Angles that form a straight line add to \(180^\circ\).

\[ 180^\circ-72^\circ=108^\circ \]

The other angle is \(108^\circ\).

Level 3: Parallel Lines and Transversals

Problem 7

Two parallel lines are cut by a transversal. A corresponding angle measures \(68^\circ\). What is the measure of the matching corresponding angle?

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Corresponding angles are congruent when lines are parallel.

\[ 68^\circ \]
Problem 8

Two parallel lines are cut by a transversal. Alternate interior angles are labeled \(4x-5\) and \(75\). Find \(x\).

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Alternate interior angles are congruent when lines are parallel.

\[ 4x-5=75 \] \[ 4x=80 \] \[ x=20 \]
Problem 9

Same-side interior angles are labeled \(x+30\) and \(2x\). The lines are parallel. Find \(x\).

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Same-side interior angles are supplementary.

\[ (x+30)+2x=180 \] \[ 3x+30=180 \] \[ 3x=150 \] \[ x=50 \]

Need more help with angle relationships?

Angle relationships become easier when students learn whether angles are equal, add to \(90^\circ\), or add to \(180^\circ\). For a full explanation, visit my Angle Relationships guide.

Related Geometry Resources

Angle Relationships Explained

Review complementary, supplementary, vertical, adjacent, and parallel-line angle rules.

Geometry Proofs

Learn how angle relationships connect to statements, reasons, and proof structure.

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