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 False
∠6 = 28°
True – ∠6 = 28°
False – ∠6 = 28°
∠5 = 28°
Based on the given information that angle ∠6 and angle ∠5 are corresponding angles due to lines A and B being parallel, we can complete the table as follows:
(1 point)
True False
∠6 = 28° False
True – ∠6 = 28° True
False – ∠6 = 28° False
∠5 = 28° True
Based on the given information that lines A and B are parallel and one angle is labeled 28°, we can deduce the following:
- ∠6 is the corresponding angle to ∠1 (as they are in the same position relative to the parallel lines). Since ∠1 is 28°, it follows that ∠6 must also be 28°. Therefore, the statement ∠6 = 28° is True.
- ∠6 is the alternate interior angle to ∠5 (as they are on opposite sides of the transversal line and inside the pair of parallel lines). Since ∠6 is 28°, it follows that ∠5 must also be 28°. Therefore, the statement ∠5 = 28° is True.
Therefore, the answers to the statements in the table are:
True
False
False
True
To complete the table, we need to determine whether each statement is true or false.
Here's how we can approach it:
1. The given angle, labeled 28°, is ∠5.
True - ∠5 = 28°
2. ∠6 is an alternate interior angle with ∠5 because lines A and B are parallel. Alternate interior angles are congruent when lines are parallel.
True - ∠6 = 28°
So the completed table would be as follows:
- ∠6 = 28°: True
- ∠6 = 28°: True
- ∠5 = 28°: True