<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />

# Same Side Interior Angles

## Angles on the same side of a transversal and inside the lines it intersects.

Estimated7 minsto complete
%
Progress
Practice Same Side Interior Angles

MEMORY METER
This indicates how strong in your memory this concept is
Progress
Estimated7 minsto complete
%
Co-Interior Angles

Learning Goal

By the end of this lesson you will be able to . . . identify co-interior 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 (co-interior) interior angle theorems to find the measure of unknown angles.

### Watch This

Watch the portions of this video dealing with same side interior angles (co-interior angles).

Then watch this video.

Finally, watch this video.

### Guidance

Same side interior angles or Co-interior 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 Co-interior 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 1800

.

#### Example A

Find z\begin{align*}z\end{align*}.

z+116=180\begin{align*}z+116^\circ=180^\circ\end{align*} so z=64\begin{align*}z = 64^\circ\end{align*} by Same Side Interior Angles Theorem.

#### Example B

Is "l" parallel to "m"? How do you know?

These angles are Co-interior Angles. So, if they add up to 180\begin{align*}180^\circ\end{align*}, then l is parallel to m.

130+67=197\begin{align*}130^\circ + 67^\circ = 197^\circ\end{align*}, therefore the lines are not parallel.

#### Example C

Give two examples of co-interior angles in the diagram below:

There are MANY examples of co-interior angles in the diagram. Two are 6\begin{align*}\angle 6\end{align*} and 10\begin{align*} \angle 10\end{align*}, and 8\begin{align*}\angle 8\end{align*} and 12\begin{align*}\angle 12\end{align*}.

### Guided Practice

1. Find the value of x\begin{align*}x\end{align*}.

2. Find the value of y\begin{align*}y\end{align*}.

3. Find the value of x\begin{align*}x\end{align*} if m3=(3x+12)\begin{align*}m\angle 3 = (3x +12)^\circ\end{align*} and  m5=(5x+8)\begin{align*}\ m\angle 5 = (5x + 8)^\circ\end{align*}.

Answers:

1. The given angles are same side interior angles. Because the lines are parallel, the angles add up to 180\begin{align*}180^\circ\end{align*}.

(2x+43)+(2x3)(4x+40)4xx=180=180=140=35\begin{align*}(2x+43)^\circ + (2x-3)^\circ & = 180^\circ\\ (4x+40)^\circ & = 180^\circ\\ 4x & = 140\\ x & =35\end{align*}

2. y\begin{align*}y\end{align*} is a same side interior angle with the marked right angle. This means that 90+y=180\begin{align*}90^\circ +y=180\end{align*} so y=90\begin{align*}y=90\end{align*}.

3. These are same side interior angles so set up an equation and solve for x\begin{align*}x\end{align*}. Remember that same side interior angles add up to 180\begin{align*}180^\circ\end{align*}.

(3x+12)+(5x+8)(8x+20)8xx=180=180=160=20\begin{align*}(3x+12)^\circ+(5x+8)^\circ&=180^\circ\\ (8x+20)^\circ&=180^\circ\\ 8x&=160\\x&=20\end{align*}

### Practice

For questions 1-2, determine if each angle pair below is congruent, supplementary or neither.

1. 5\begin{align*}\angle 5\end{align*} and 8\begin{align*}\angle 8\end{align*}
2. 2\begin{align*}\angle 2\end{align*} and 3\begin{align*}\angle 3\end{align*}
3. Are the lines below parallel? Justify your answer.

In 4-5, use the given information to determine which lines are parallel. If there are none, write none. Consider each question individually.

1. AFD\begin{align*}\angle AFD\end{align*} and BDF\begin{align*}\angle BDF\end{align*} are supplementary
2. \begin{align*}\angle DIJ\end{align*} and \begin{align*}\angle FJI\end{align*} are supplementary

For 6-8, what does the value of \begin{align*}x\end{align*} have to be to make the lines parallel?

1. \begin{align*}m\angle 3 = (3x+25)^\circ\end{align*} and \begin{align*}m\angle 5 = (4x-55)^\circ\end{align*}
2. \begin{align*}m\angle 4 = (2x+15)^\circ\end{align*} and \begin{align*}m\angle 6 = (3x-5)^\circ\end{align*}
3. \begin{align*}m\angle 3 = (x+17)^\circ\end{align*} and \begin{align*}m\angle 5 = (3x-5)^\circ\end{align*}

For 9-10, determine whether the statement is true or false.

1. Same side interior angles are on the same side of the transversal.
2. Same side interior angles are congruent when lines are parallel.

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / Notes
Show More

### Explore More

Sign in to explore more, including practice questions and solutions for Same Side Interior Angles.
Please wait...
Please wait...