In the figure, one angle is labeled 28°
, and lines A
and B
are parallel. Complete the table. For each statement, select True or False.
(1 point)
True or False
∠6 = 28°
∠5 = 28°
Based on the given information, we can conclude the following:
1) ∠6 = 28° - False. In the figure, ∠6 and ∠1 are corresponding angles, and since lines A and B are parallel, corresponding angles are congruent. Therefore, ∠6 is also 28°.
2) ∠5 = 28° - False. In the figure, ∠5 and ∠2 are alternate interior angles, and since lines A and B are parallel, alternate interior angles are congruent. Therefore, ∠5 is not necessarily 28°.
Based on the information given, we can analyze the statements:
∠6 = 28° - Since ∠6 and ∠5 are alternate interior angles and lines A and B are parallel, we can conclude that ∠6 = 28°. Therefore, the statement is True.
∠5 = 28° - Since ∠5 and ∠6 are alternate interior angles and lines A and B are parallel, we can conclude that ∠5 = 28°. Therefore, the statement is True.
So, both statements are True.
To determine whether each statement is True or False, we need to use the properties of parallel lines and angles.
1. ∠6 = 28°:
To find the measure of ∠6, we can use the fact that corresponding angles formed by a transversal and parallel lines are congruent. In this case, line A and line B are parallel, and ∠5 and ∠6 are corresponding angles.
If ∠5 = 28°, then ∠6 must also be 28°. Therefore, this statement is True.
2. ∠5 = 28°:
The measure of ∠5 is explicitly given as 28° in the problem. Therefore, this statement is also True.
So, the answers for each statement are:
∠6 = 28°: True
∠5 = 28°: True