Learning Goal
By the end of this lesson you will be able to . . . identify cointerior angles and use your knowledge to find missing angle measures.
What if you were presented with two angles that are on the same side of the transversal and on the interior of the two lines? How would you describe these angles and what could you conclude about their measures? After completing this Concept, you'll be able to answer these questions and apply same side (cointerior) interior angle theorems to find the measure of unknown angles.
Watch This
CK12 Same Side Interior Angles
Watch the portions of this video dealing with same side interior angles (cointerior angles).
James Sousa: Angles and Transversals
Then watch this video.
James Sousa: Proof that Consecutive Interior Angles Are Supplementary
Finally, watch this video.
James Sousa: Proof of Consecutive Interior Angles Converse
Guidance
Same side interior angles or Cointerior angles are two angles that are on the same side of the transversal and on the interior of the two lines.
Same Side Interior Angles Theorem or Cointerior Angle Theorem: If two parallel lines are cut by a transversal, then the same side interior angles are supplementary.
If line "l" is parallel to "m", then angle 1 and angle 2 add up to 180^{0}
.
Example A
Find \begin{align*}z\end{align*}
\begin{align*}z+116^\circ=180^\circ\end{align*}
Example B
Is "l" parallel to "m"? How do you know?
These angles are Cointerior Angles. So, if they add up to \begin{align*}180^\circ\end{align*}
\begin{align*}130^\circ + 67^\circ = 197^\circ\end{align*}
Example C
Give two examples of cointerior angles in the diagram below:
There are MANY examples of cointerior angles in the diagram. Two are \begin{align*}\angle 6\end{align*}
CK12 Same Side Interior Angles
Guided Practice
1. Find the value of \begin{align*}x\end{align*}
2. Find the value of \begin{align*}y\end{align*}
3. Find the value of \begin{align*}x\end{align*}
Answers:
1. The given angles are same side interior angles. Because the lines are parallel, the angles add up to \begin{align*}180^\circ\end{align*}
\begin{align*}(2x+43)^\circ + (2x3)^\circ & = 180^\circ\\
(4x+40)^\circ & = 180^\circ\\
4x & = 140\\
x & =35\end{align*}
2. \begin{align*}y\end{align*}
3. These are same side interior angles so set up an equation and solve for \begin{align*}x\end{align*}
\begin{align*}(3x+12)^\circ+(5x+8)^\circ&=180^\circ\\ (8x+20)^\circ&=180^\circ\\ 8x&=160\\x&=20\end{align*}
Practice
For questions 12, determine if each angle pair below is congruent, supplementary or neither.

\begin{align*}\angle 5\end{align*}
∠5 and \begin{align*}\angle 8\end{align*}∠8 
\begin{align*}\angle 2\end{align*}
∠2 and \begin{align*}\angle 3\end{align*}∠3  Are the lines below parallel? Justify your answer.
In 45, use the given information to determine which lines are parallel. If there are none, write none. Consider each question individually.

\begin{align*}\angle AFD\end{align*}
∠AFD and \begin{align*}\angle BDF\end{align*}∠BDF are supplementary  \begin{align*}\angle DIJ\end{align*} and \begin{align*}\angle FJI\end{align*} are supplementary
For 68, what does the value of \begin{align*}x\end{align*} have to be to make the lines parallel?
 \begin{align*}m\angle 3 = (3x+25)^\circ\end{align*} and \begin{align*}m\angle 5 = (4x55)^\circ\end{align*}
 \begin{align*}m\angle 4 = (2x+15)^\circ\end{align*} and \begin{align*}m\angle 6 = (3x5)^\circ\end{align*}
 \begin{align*}m\angle 3 = (x+17)^\circ\end{align*} and \begin{align*}m\angle 5 = (3x5)^\circ\end{align*}
For 910, determine whether the statement is true or false.
 Same side interior angles are on the same side of the transversal.
 Same side interior angles are congruent when lines are parallel.