Question

finding an angle measure
what is the measure of $\angle$edh?
$\circ$ $10^\circ$
$\circ$ $40^\circ$
$\circ$ $50^\circ$
$\circ$ $90^\circ$

Explanation:

Step1: Identify the right triangle

In triangle \(EDH\), we know that \(\angle E\) is a right angle (\(90^\circ\)), so the sum of \(\angle EDH\) (\(5x\)) and \(\angle DHE\) (\(4x\)) should be \(90^\circ\) (since the sum of angles in a triangle is \(180^\circ\) and one angle is \(90^\circ\)). So we set up the equation \(5x + 4x=90\).

Step2: Solve for \(x\)

Combine like terms: \(9x = 90\). Then divide both sides by 9: \(x=\frac{90}{9} = 10\).

Step3: Find the measure of \(\angle EDH\)

We know \(\angle EDH = 5x\). Substitute \(x = 10\) into the expression: \(5\times10=50^\circ\).

Answer:

\(50^\circ\) (corresponding to the option \(50^\circ\))