Example Question - alternate interior angles
Here are examples of questions we've helped users solve.
Finding the Value of x in Parallel Line Segments with Given Angle Expressions
\begin{align*} \text{Let } \angle ABC &= \angle BAC \text{ (alternate interior angles are equal because } AD \parallel BC) \\ 4x + 30^\circ &= 40^\circ \\ 4x &= 10^\circ \\ x &= \frac{10^\circ}{4} \\ x &= 2.5^\circ \\ \end{align*} \text{Round to the nearest tenth: } x = 2.5^\circ
Determining Parallel Lines Using Alternate Interior Angles
The image shows two lines cut by a transversal, with two angles labeled as \( m \angle 4 \) and \( m \angle 7 \). We are told that \( m \angle 4 = m \angle 7 \). This means angle 4 and angle 7 are congruent. Using this information, we can determine which lines are parallel. Congruent corresponding angles, which occur when a transversal crosses two parallel lines, imply that the lines are indeed parallel. In this case, angle 4 and angle 7 are alternate interior angles. According to the Alternate Interior Angles Theorem, if alternate interior angles are congruent, then the lines are parallel. So, the correct answer is: \[ \bar{t} || \bar{m}, \text{ by the Converse of the Alternate Interior Angles Theorem.} \] This is the third option in the list provided in the image.
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