Let's go through the exercise you've uploaded. The main goal is to evaluate each statement, decide if it's true or false, and then write its negation and check the negated truth value.

Here's the structure of what we need to solve for Exercises 1-6:

Given Diagram Information:

• $m\angle BAC = 90^\circ$
• $\angle B = 127^\circ$
• $\angle 2 = 53^\circ$

Statements:

1. $m\angle BAC = 90^\circ$

   • True or False?: True, because it's given that $m\angle BAC$ forms a right angle.
   • Negation (~p): $m\angle BAC \neq 90^\circ$
   • True or False?: False, since the original statement is true.

2. $\angle B$ is obtuse.

   • True or False?: True, as $\angle B = 127^\circ$, and angles greater than 90° and less than 180° are obtuse.
   • Negation (~p): $\angle B$ is not obtuse.
   • True or False?: False, because the original statement is true.

3. $\angle 1$ is a complement of $\angle 2$.

   • True or False?: False. The sum of complementary angles must equal 90°, but $\angle 1 + \angle 2 = 90^\circ$ is not given.
   • Negation (~p): $\angle 1$ is not a complement of $\angle 2$.
   • True or False?: True, because the original statement is false.

4. $\angle 2$ is a supplement of $\angle B$.

   • True or False?: True, because supplementary angles sum up to 180°, and $127^\circ + 53^\circ = 180^\circ$.
   • Negation (~p): $\angle 2$ is not a supplement of $\angle B$.
   • True or False?: False, since the original statement is true.

5. $m\angle 1 + m\angle 2 = 180^\circ$

   • True or False?: False, because $\angle 1 + \angle 2 = 90^\circ$, not 180°.
   • Negation (~p): $m\angle 1 + m\angle 2 \neq 180^\circ$
   • True or False?: True, since the original statement is false.

6. $\overrightarrow{AX}$ is a bisector of $\angle BAC$.

   • True or False?: True, based on the diagram, $\overrightarrow{AX}$ divides $\angle BAC$ into two equal parts.
   • Negation (~p): $\overrightarrow{AX}$ is not a bisector of $\angle BAC$.
   • True or False?: False, since the original statement is true.

Would you like a deeper explanation of any of these? Let me know if you'd like assistance with the next set of exercises!

Here are 5 related questions for further understanding:

1. What is the definition of complementary angles?
2. How can we identify an obtuse angle in any triangle or geometric figure?
3. What conditions must two angles satisfy to be called supplementary?
4. How do we verify if a line bisects an angle?
5. What properties do perpendicular bisectors have in a geometric figure?

Tip:

Always remember, the negation of a statement reverses the truth value of the original. When practicing, it's important to verify the truth value of both the statement and its negation!