Question
Two parallel lines L1 and L2 are cut by a transversal. If one of the alternate interior angles is $65^\circ$, what is the measure of the corresponding alternate interior angle?
The correct answer is
$65^\circ$
Parallel Lines Transversal Property
When two parallel lines, L1 and L2, are intersected by a transversal line, specific angle relationships are formed. A key property is that alternate interior angles are equal.
Determining Alternate Interior Angle Measure
The problem states that one of the alternate interior angles measures $65^\circ$.
Based on the geometric principle that alternate interior angles formed by parallel lines and a transversal are congruent (equal in measure):
- If one alternate interior angle = $65^\circ$
- Then the other alternate interior angle must also equal $65^\circ$.
Thus, the measure of the corresponding alternate interior angle is $65^\circ$.
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Important Questions from Lines and Angles
- Two lines AB and CD are parallel. Let PQ be the transversal intersecting AB at M and CD at N. If $\angle MND = 47^\circ$, find $\angle AMN$.
- The measure of an angle is one half of its supplementary angle. Find its measure.
- The sum of two angles is $155^\circ$ and their difference is $\frac{\pi}{2}$. The value of the greater angle (in radians) is:
- The measure of an angle is three times the measure of its complement. The angles are respectively:
- The supplement of $70^\circ$ is:
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