Question

multiple choice 3 points
a carpenter nailed a board across two beams as shown in the picture below. which angles should be equal to ensure the beams are parallel?
<2 = <5
<2 = <3
<4 = <6
<1 = <3

Explanation:

Step1: Recall the alternate - interior angles theorem

If two lines are cut by a transversal and the alternate - interior angles are equal, then the two lines are parallel.

Step2: Analyze each option

• For \(\angle2=\angle5\): These are not alternate - interior angles.
• For \(\angle2 = \angle3\): These are vertical angles (not related to the parallel - line criteria).
• For \(\angle4=\angle6\): These are not alternate - interior angles.
• For \(\angle1=\angle3\): \(\angle1\) and \(\angle3\) are alternate - interior angles. If \(\angle1=\angle3\), by the alternate - interior angles theorem, the two beams (lines) are parallel.

Answer:

\(\angle1=\angle3\) (the fourth option)