Answer:
Vertically opposite angles are [tex]x,z;y,76^{\circ}[/tex]
Linear pair of angles are [tex]x,y;y,z;z,76^{\circ};x,76^{\circ}[/tex]
[tex]y=76^{\circ}[/tex], [tex]z=x=104^{\circ}[/tex]
Step-by-step explanation:
Given: image
To find: vertical angles, the angles that form linear pairs, value of x, y and z
Solution:
If two lines intersect each other then the vertically angles formed are equal.
Two adjacent angles are said to be linear if their sum is [tex]180^{\circ}[/tex].
From the given image,
vertically opposite angles are [tex]x,z;y,76^{\circ}[/tex]
Linear pair of angles are [tex]x,y;y,z;z,76^{\circ};x,76^{\circ}[/tex]
As vertically opposite angles are equal, [tex]y=76^{\circ}[/tex]
As sum of angles that form a linear pair is [tex]180^{\circ}[/tex],
[tex]x+76^{\circ}=180^{\circ}\\x=180^{\circ}-76^{\circ}\\=104^{\circ}[/tex]
Also, as x and z are vertically opposite angles,
[tex]z=x=104^{\circ}[/tex]
