Trapezoid v3

The isosceles trapezoid has an angle at the first base 40 degrees less than the angle at the second base. How large angles has this trapezoid?

Final Answer:

α =  70 °
β =  110 °
γ =  110 °
δ =  70 °

Step-by-step explanation:

$$\begin{gathered} \alpha =\delta \\ \beta =\gamma \\ \alpha +\beta +\gamma +\delta =360{}^{\circ } \\ \alpha +\beta +\beta +\alpha =360{}^{\circ } \\ \alpha +\beta =180{}^{\circ } \\ \alpha +40=\beta \\ \alpha +(\alpha +40)=180 \\ 2\alpha =140 \\ \alpha =\frac{140}{2}=70 \\ \alpha =70=70^{\circ } \end{gathered}$$

$\beta =\alpha +40=70+40=110^{\circ }$

$\gamma =\beta =110=110^{\circ }$

$\delta =\alpha =70=70^{\circ }$

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