Question

find ( mangle e ).
( mangle e = square^circ )

Explanation:

Step1: Identify sides for ∠E

For $\angle E$, opposite side $CD = 2\sqrt{30}$, adjacent side $ED = 2\sqrt{10}$.

Step2: Use tangent ratio

$\tan(\angle E) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2\sqrt{30}}{2\sqrt{10}}$
Simplify: $\tan(\angle E) = \sqrt{\frac{30}{10}} = \sqrt{3}$

Step3: Solve for ∠E

Find angle whose tangent is $\sqrt{3}$: $\angle E = \arctan(\sqrt{3})$

Answer:

$60$