Question

find x
(7x - 25)°
3y + 11
*ef = 10√2
find y

Explanation:

Step1: Set angle equal to 90°

In a square, all interior angles are $90^\circ$. So:
$$7x - 25 = 90$$

Step2: Solve for x

Isolate $x$ by first adding 25 to both sides, then dividing by 7:
$$7x = 90 + 25 = 115$$
$$x = \frac{115}{7} \approx 16.43$$

Step3: Relate diagonal segment to side

In a square, the length of a diagonal is $s\sqrt{2}$ where $s$ is the side length. The segment $EF$ is half the diagonal, so full diagonal $= 2 \times 10\sqrt{2} = 20\sqrt{2}$. Set equal to $s\sqrt{2}$:
$$s\sqrt{2} = 20\sqrt{2}$$
$$s = 20$$

Step4: Solve for y

Set the side expression equal to 20:
$$3y + 11 = 20$$
$$3y = 20 - 11 = 9$$
$$y = \frac{9}{3} = 3$$

Answer:

$x = \frac{115}{7}$, $y = 3$