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

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

You may start by drawing a sketch.

Compute $\alpha \backslash alpha$ using the tangent.

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

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

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

$\alpha ={21.3}^{\circ }\backslash alpha=21.3^\{\backslash circ\}$

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

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

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

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

Required: $\gamma ,\delta \backslash gamma,\backslash ;\backslash delta$

You may start by drawing a sketch.

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

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

$\Rightarrow \backslash Rightarrow$ $\delta \backslash delta$ $==$$22$ $\alpha \backslash alpha$

$\delta =2\cdot {68.7}^{\circ }={137.4}^{\circ }\backslash delta=2\backslash cdot68.7^\{\backslash circ\}=137.4^\{\backslash circ\}$

$\gamma \backslash gamma$ and $\delta \backslash delta$ add up to 180°.

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

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