Question

find the largest angle of $\triangle cde$. assume that $s$ is a positive number.

Explanation:

Step1: Identify side lengths

Sides: $ED=8s$, $DC=22s$, let $EC=x$

Step2: Compare known side lengths

Since $s>0$, $22s > 8s$, so $DC > ED$.

Step3: Relate sides to opposite angles

In a triangle, the longest side is opposite the largest angle. Side $ED$ is opposite $\angle C$, side $DC$ is opposite $\angle E$, and side $EC$ is opposite $\angle D=97^\circ$.

Step4: Analyze angle magnitudes

$\angle D=97^\circ$ is an obtuse angle. The sum of the other two angles is $180^\circ - 97^\circ=83^\circ$, so both $\angle E$ and $\angle C$ are acute (less than $90^\circ$).

Answer:

$\angle D$ (or $97^\circ$)