Answer:
In the given diagram, we are told that angle ZXWZ is 90 degrees. We need to find the value of angle X.
We can start by using the fact that the sum of angles in a straight line is 180 degrees. Since angles Z and W are adjacent and add up to 180 degrees, we can write:
Z + W = 180
Next, we can use the information given about angles Y, Z, and W. We know that the measure of angle Y is (5x + 5) degrees and the measure of angle Z is -(2x + 8) degrees. So we can write:
Y + Z + W = 180
Substituting the given expressions for angles Y and Z, we have:
(5x + 5) + (-(2x + 8)) + W = 180
Simplifying this equation, we get:
5x + 5 - 2x - 8 + W = 180
Combining like terms, we have:
3x - 3 + W = 180
Next, we use the information that angle ZXWZ is 90 degrees. This means that the sum of angles Z and W is 90 degrees. So we can write:
Z + W = 90
Substituting this equation into our previous equation, we get:
3x - 3 + (Z + W) = 180
Simplifying further, we have:
3x - 3 + 90 = 180
Combining like terms, we get:
3x + 87 = 180
To solve for x, we can subtract 87 from both sides:
3x = 180 - 87
3x = 93
Dividing both sides by 3, we find:
x = 31
Therefore, the value of x is 31.