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
∠5 = 28°
True – ∠5 = 28°
False – ∠5 = 28°
∠6 = 28°
True – ∠6 = 28°
False – ∠6 = 28°
The given information is not sufficient to complete the table. Can you provide more details or a diagram?
Based on the given information, we can determine the following:
(1) ∠5 = 28°: True
Since lines A and B are parallel, ∠5 and ∠6 are corresponding angles and they are congruent.
(2) ∠5 = 28°: False
This statement contradicts our previous statement, as we just established that ∠5 = 28° is true.
(3) ∠5 = 28°: False
Again, this statement contradicts our first statement and is therefore false.
(4) ∠6 = 28°: True
As mentioned earlier, ∠5 and ∠6 are corresponding angles and congruent, so if ∠5 = 28°, then ∠6 must also equal 28°.
(5) ∠6 = 28°: True
This statement reiterates what we determined in the previous one, so it is true.
(6) ∠6 = 28°: False
Once again, this statement contradicts our earlier conclusion that ∠6 = 28° is true.
To determine the correct answers for each statement, we need to understand the properties of parallel lines and angles.
When two lines are parallel, the corresponding angles formed by a transversal (a line that intersects the parallel lines) are congruent. This means that if one angle measures 28°, the corresponding angle will also measure 28°.
Now let's complete the table:
∠5 = 28°: This statement is false. While one angle is labeled 28°, we cannot conclude that ∠5 is also 28°. We would need additional information or angle measurements to determine the value of ∠5.
True – ∠5 = 28°: Since the previous statement is false, this statement is also false. We cannot say that ∠5 is equal to 28°.
False – ∠5 = 28°: This statement is correct, as we cannot determine the value of ∠5 based on the given information.
∠6 = 28°: This statement is true. Since the lines are parallel, the corresponding angles formed by the transversal are congruent. Therefore, if one angle measures 28°, ∠6 will also measure 28°.
True – ∠6 = 28°: Since the previous statement is true, this statement is correct. ∠6 is indeed equal to 28° based on the given information.
False – ∠6 = 28°: This statement is false. We can conclude that ∠6 is indeed equal to 28°.
In summary, the correct answers are:
∠5 = 28°: False
True – ∠5 = 28°: False
False – ∠5 = 28°: True
∠6 = 28°: True
True – ∠6 = 28°: True
False – ∠6 = 28°: False