kent408
kent408 Jan 15, 2026 • 0 views

Solved Examples of Consecutive Interior Angles Theorem Problems

Hey there! 👋 Struggling with consecutive interior angles? No worries, I've got you covered. Check out this quick guide and quiz to boost your skills! 💯
🧮 Mathematics
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📚 Quick Study Guide

  • 📐 Definition: Consecutive interior angles are pairs of angles that lie on the same side of the transversal and between the two lines it intersects.
  • 🤝 Theorem: If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary (their measures add up to 180 degrees).
  • ✏️ Formula: If $l \parallel m$, then $m\angle 1 + m\angle 2 = 180^{\circ}$, where $\angle 1$ and $\angle 2$ are consecutive interior angles.
  • 💡 Key Idea: Look for the 'C' shape formed by the parallel lines and the transversal to easily identify consecutive interior angles.
  • Supplementary Angles: Remember that supplementary angles add up to $180^{\circ}$. This is crucial for solving problems.

Practice Quiz

  1. What is the relationship between consecutive interior angles when two parallel lines are cut by a transversal?
    1. They are congruent.
    2. They are complementary.
    3. They are supplementary.
    4. They are vertical.

  2. If two parallel lines are intersected by a transversal and one of the consecutive interior angles measures 60°, what is the measure of the other angle?
    1. 30°
    2. 60°
    3. 120°
    4. 150°

  3. In the diagram below, lines $a$ and $b$ are parallel. If $m\angle 1 = 110^{\circ}$, what is $m\angle 2$, where $\angle 1$ and $\angle 2$ are consecutive interior angles?
    1. 60°
    2. 70°
    3. 80°
    4. 90°

  4. Lines $p$ and $q$ are parallel, cut by a transversal $t$. If one of the consecutive interior angles is twice the size of the other, what is the measure of the smaller angle?
    1. 30°
    2. 45°
    3. 60°
    4. 90°

  5. If consecutive interior angles measure $(3x + 10)^{\circ}$ and $(2x + 30)^{\circ}$, and the lines are parallel, what is the value of $x$?
    1. 20
    2. 28
    3. 30
    4. 35

  6. In a diagram, two parallel lines are cut by a transversal. One of the consecutive interior angles is a right angle. What is the measure of the other consecutive interior angle?
    1. 30°
    2. 45°
    3. 60°
    4. 90°

  7. Lines $m$ and $n$ are parallel. If one angle measures $x$ and the other consecutive interior angle measures $5x$, find the value of $x$.
    1. 15
    2. 30
    3. 45
    4. 60
Click to see Answers
  1. C
  2. C
  3. B
  4. C
  5. B
  6. D
  7. B

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