Question

finding an angle measure what is the measure of ∠edh? (5x)° (4x)° 10° 50° 90° 40°

Explanation:

Step1: Use angle - sum property of right - angle

In right - triangle $EDG$, $\angle EDG = 90^{\circ}$, and $\angle EDG=\angle EDH+\angle HDG$. So, $5x + 4x=90$.

Step2: Solve the equation for $x$

Combining like terms, we get $9x = 90$. Then, dividing both sides by 9, $x=\frac{90}{9}=10$.

Step3: Find the measure of $\angle EDH$

Since $\angle EDH = 5x$, substituting $x = 10$ into the expression, we have $\angle EDH=5\times10 = 50^{\circ}$.

Answer:

$50^{\circ}$