Question

finding an angle measure
what is the measure of $angle edh$
$\bigcirc$ $10^circ$
$\bigcirc$ $40^circ$
$\bigcirc$ $50^circ$
$\bigcirc$ $90^circ$
$(5x)^circ$
$(4x)^circ$

Explanation:

Step1: Set up angle sum equation

In rectangle \(DEFG\), \(\angle EDG = 90^\circ\), so \(\angle EDH + \angle HDG = 90^\circ\). Substitute the given angle expressions:
\(5x + 4x = 90\)

Step2: Solve for \(x\)

Combine like terms and isolate \(x\):
\(9x = 90\)
\(x = \frac{90}{9} = 10\)

Step3: Calculate \(\angle EDH\)

Substitute \(x=10\) into \(5x\):
\(\angle EDH = 5 \times 10 = 50\)

Answer:

50°