Solved Examples of Consecutive Interior Angles Theorem Problems

📚 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