Given: $a=7\;\text{cm}$; $b= 18\;\text{cm}$

Required: $\alpha,\;\beta,\;$

You may start by drawing a sketch.

Compute $\alpha$ using the tangent.

$\tan\left(\alpha\right)=\frac{a}{b}$

Insert the values and calculate $\alpha$ using the calculator.

$\tan(\alpha)=\frac{7\text{cm}}{18\text{cm}}$

$\alpha=21.3^{\circ}$

Compute $\beta$. $\alpha$ and $\beta$ add up to 90° , so for $\beta$, we have:

$\beta=90^{\circ}-21{,}3^{\circ}=68.7^{\circ}$

$\Rightarrow$ The angle $\alpha$ is 21.3°. $\beta$ equals 68.7°.

Given: $\alpha=68.7^\circ;\;\beta=21.3^\circ$

Required: $\gamma,\;\delta$

You may start by drawing a sketch.

$\delta$ equals 2 $\alpha$ , since $\delta$ $+$ $\gamma$ $=$180° and $\gamma$ $+2$ $\alpha$ $=$180° holds in a right triangle.

$\Rightarrow$ $\delta$ + $\gamma$ $=$ $\gamma$ $+2$ $\alpha$

$\Rightarrow$ $\delta$ $=$$2$ $\alpha$

$\delta=2\cdot68.7^{\circ}=137.4^{\circ}$

$\gamma$ and $\delta$ add up to 180°.

$\gamma=180^{\circ}-137.4^{\circ}=42.6^{\circ}$

$\Rightarrow$ The angle  $\gamma$ equals 42,6°.  $\delta$ amounts to 137.4°.