Question

Find the values of x and z

Answer 1

z = 69 and x = 7

Explanation:

In this image, we have a line cut by a transversal, we know that when a line is cut by a transversal, the sum of two adjacent angles is 180º

Using this in the image we have that 111 + z = 180. We are going to solve for z.

`111 + z = 180\\z= 180 -11\\z= 69`

Therefore z = 69.

Using the same property for the other two other adjacents angles we have that z + (11x + 34) = 180.

But since z = 69 we have:

`z + (11x+34)=180\\69 +11x+34=180\\11x=180-34-69\\11x= 77\\x= 7`

Therefore x = 7

Answer 2

z = 7 and z = 69

Explanation:

In the given figure, two lines are cut each other.

Here we have to use the following property.

If the two lines intersect each other, then the opposite sides are equal.

Therefore, 11x + 34 = 111

Now we have to find the value of x.

Solve for x.

11x = 111 - 34

11x = 77

Dividing both sides by 11, we get

x = 77/11

x = 7

Now we have to find the value of z.

Adjacent angles add upto 180 in a straight line.

Therefore, 111 + z = 180

Subtract 111 on both sides, we get

111 + z -111 = 180 - 111

z = 69

Therefore, z = 7 and z = 69

Hope you will understand the concept.

Thank you.