Question

for what value of x is the figure a rectangle?
(5x + 2)°
3x°
x = \square (simplify your answer)

Explanation:

Step1: Use rectangle diagonal property

In a rectangle, diagonals are equal and bisect each other, so the triangle formed is isosceles, and the adjacent angles along the diagonal are complementary (they form a right angle of the rectangle). Thus:
$$3x + (2x + 2) = 90$$

Step2: Combine like terms

Add the x terms and constants:
$$5x + 2 = 90$$

Step3: Isolate the variable term

Subtract 2 from both sides:
$$5x = 90 - 2 = 88$$

Step4: Solve for x

Divide both sides by 5:
$$x = \frac{88}{5} = 17.6$$

Answer:

$17.6$ or $\frac{88}{5}$