Answer:
[tex]x^{\circ}+105^{\circ}=180^{\circ},\\x^{\circ}=z^{\circ},\\180^{\circ}-z^{\circ}=y^{\circ}[/tex]
Step-by-step explanation:
Statement 1:
True - These two angles are supplementary (add up to 180 degrees) because they form one side of a line.
Statement 2:
True - These two angles are vertical angles (opposite to each other at intersection of two lines). All vertical angles are equal.
Statement 3:
False - These two angles are vertical and therefore are equal. Thus, they cannot have a difference of 105.
Statement 4:
False - Two of these angles form one side of a line which is equal to 180 degrees. Since the third angle is greater than zero, they cannot all add up to 180 degrees.
Statement 5:
True - These two angles are supplementary (add up to 180 degrees) because they form one side of a line.
Statement 6:
False - These two angles are supplementary (add up to 180 degrees) because they form one side of a line and therefore cannot be equal to 105.
