Question

Using the image below, identify the angles that are vertical angles, list the angles that are linear pairs, and then solve for , , and .

Answer 1

Answer:

Vertically opposite angles are $x,z;y,76^{\circ}$

Linear pair of angles are $x,y;y,z;z,76^{\circ};x,76^{\circ}$

$y=76^{\circ}$, $z=x=104^{\circ}$

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 $180^{\circ}$.

From the given image,

vertically opposite angles are $x,z;y,76^{\circ}$

Linear pair of angles are $x,y;y,z;z,76^{\circ};x,76^{\circ}$

As vertically opposite angles are equal, $y=76^{\circ}$

As sum of angles that form a linear pair is $180^{\circ}$,

$x+76^{\circ}=180^{\circ}\\x=180^{\circ}-76^{\circ}\\=104^{\circ}$

Also, as x and z are vertically opposite angles,

$z=x=104^{\circ}$