Question

in the square below, $m\angle qhe = (-6x - 24) ^\circ$. find $x$.

Explanation:

Step1: Recall square angle property

In a square, the diagonal bisects the right angle, so \( \angle QHE = 45^\circ \).

Step2: Set up equation

We know \( m\angle QHE = (-6x - 24)^\circ \) and \( \angle QHE = 45^\circ \), so:
\( -6x - 24 = 45 \)

Step3: Solve for x

Add 24 to both sides:
\( -6x = 45 + 24 \)
\( -6x = 69 \)
Divide both sides by -6:
\( x = \frac{69}{-6} = -\frac{23}{2} = -11.5 \)

Answer:

\( x = -11.5 \)