KLMN

In the KLMN trapezoid is given this information:
1. segments KL and MN are parallel
2. segments KL and KM have the same length
3. segments KN, NM, and ML have the same length.

Determine the size of the angle KMN.

Correct answer:

α =  36 °

Step-by-step explanation:

$$\begin{gathered} |KL|=|KM| \\ |KN|=|NM|=|ML| \\ \alpha =\sphericalangle KMN=\sphericalangle NKM=\sphericalangle MKL \\ \beta =\sphericalangle KNM \\ \sphericalangle KML=\beta -\alpha \\ \sphericalangle KLM=180°-\alpha -(\beta -\alpha )=180°-\beta \\ \Delta KLM: \\ \sphericalangle KML=\sphericalangle KLM \\ \beta -\alpha =180°-\beta \\ \beta =180°+\alpha /2; \\ \Delta KMN: \\ 2\alpha +\beta =180° \\ 2\alpha +90+\alpha /2=180° \\ 2.5\alpha =90° \\ \alpha =36^{\circ } \end{gathered}$$

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