Question

in the square below, $m\angle shp = (-2x - 28) ^\circ$. find $x$.

Explanation:

Step1: Recall square angle property

In a square, each angle is \(90^\circ\), and the diagonal bisects the angle, so \(\angle SHP = 45^\circ\).

Step2: Set up equation

We know \(m\angle SHP = (-2x - 28)^\circ\) and \(\angle SHP = 45^\circ\), so:

$$ -2x - 28 = 45 $$

Step3: Solve for \(x\)

Add 28 to both sides:

$$ -2x = 45 + 28 $$

$$ -2x = 73 $$

Divide both sides by -2:

$$ x = -\frac{73}{2} = -36.5 $$

Answer:

\(x = -36.5\)