Answer:
x = 13.4
Step-by-step explanation:
In a rectangle, opposite angles are equal, and the sum of all angles is 360 degrees. Additionally, in a rectangle, each angle at a corner is a right angle, meaning it measures 90 degrees.
Let's consider the rectangle ABCD. In a rectangle, opposite angles are equal, so ∠B is equal to ∠D, and ∠A is equal to ∠C.
We have:
∠B = 8x - 17.
Since ∠B is a right angle (∠B = 90° in a rectangle), we can set up an equation to solve for x:
[tex] 8x - 17 = 90 [/tex]
Now, solve for x:
[tex] 8x = 90 + 17 [/tex]
[tex] 8x = 107 [/tex]
[tex] x = \dfrac{107}{8} [/tex]
[tex] x = 13.375 [/tex]
[tex] x = 13.4 \textsf{(in one decimal place)}[/tex]
So, the value of x is 13.4.
