Example Question - alternate exterior angles
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Determining Angle Measures with Parallel Lines and a Transversal
The image displays two parallel lines (labeled l and m) with a transversal cutting across them. There are two angles marked on the transversal, one is x degrees and the other is 16x degrees. Since the lines l and m are parallel, and the angle of 16x degrees is an alternate exterior angle to the angle x degrees, these two angles are congruent according to the Alternate Exterior Angles Theorem. Therefore, we can write the following equation: x = 16x To solve for x, we'll need to move terms around to isolate x: x - 16x = 0 Combine like terms: -15x = 0 Divide both sides by -15: x = 0/-15 x = 0 So, the value of x is 0 degrees. However, this is a unique situation, as angles typically measure a positive angle between two lines. It would be unusual for an angle to have a measure of 0 degrees unless the lines were consistent with being the same line, which does not appear to be the case in the image. This result suggests that there might be a mistake in the angle labels or that additional context is needed to solve the problem appropriately.
Lines and Angles
The diagram shows two lines, line \( l \) and line \( m \), cut by a transversal line \( r \). According to the information provided, \( m\angle2 = m\angle7 \). Angles 2 and 7 are alternate exterior angles. If the measures of alternate exterior angles are equal, then by the Converse of the Alternate Exterior Angles Theorem, the lines are parallel. So, the correct answer is: D) \( l \parallel m \), by the Converse of the Same-Side Interior Angles Postulate. However, please be aware there's an inconsistency between the answer and the justification in the options provided. Answer D incorrectly states "Same-Side Interior Angles Postulate" as the justification, when it should be "Alternate Exterior Angles Theorem" for the reason discussed.
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