Question

for what values of x is the figure a rectangle?
...
(4x + 7)°
6x°
x = \square (simplify your answer)

Explanation:

Step1: Use rectangle diagonal property

In a rectangle, diagonals are congruent and bisect each other, forming isosceles triangles. Also, the angle between a side and diagonal and the adjacent angle from the other diagonal add to 90° (since rectangle angles are 90°). So:
$$4x + (4x + 2) = 90$$

Step2: Combine like terms

Simplify the left-hand side:
$$8x + 2 = 90$$

Step3: Isolate the variable term

Subtract 2 from both sides:
$$8x = 88$$

Step4: Solve for x

Divide both sides by 8:
$$x = \frac{88}{8} = 11$$

Answer:

$11$