Quadrilateral 7583

For the sizes of the interior angles of the quadrilateral ABCD, the following applies: the angle alpha is 26° greater than the angle beta, twice the angle Beta is 5° less than the angle gamma, and the angle gamma is 36° greater than the angle delta. Determine the angles.

Final Answer:

α =  86 °
β =  60 °
γ =  125 °
δ =  89 °

Step-by-step explanation:

$$\begin{gathered} \alpha =26+\beta \\ 2\cdot \beta =\gamma -5 \\ \gamma =36+\delta \\ \alpha +\beta +\gamma +\delta =360 \\ (26+\beta )+\beta +(36+\delta )+\delta =360 \\ 2\cdot \beta =(36+\delta )-5 \\ 2\beta +2\delta =298 \\ 2\beta -\delta =31 \\ Row2-Row1\to Row2 \\ -3\delta =-267 \\ \delta =\frac{-267}{-3}=89 \\ \beta =\frac{298-2\delta }{2}=\frac{298-2\cdot 89}{2}=60 \\ \beta =60 \\ \delta =89 \\ \alpha =26+\beta =26+60=86^{\circ } \end{gathered}$$

$\gamma =36+\delta =36+89=125^{\circ }$

Try another example