Acute triangle

In the acute triangle KLM, V is the intersection of its heights and X is the heel of height to the side KL. The axis of the angle XVL is parallel to the side LM and the angle MKL is 70°. What size are the KLM and KML angles?

Correct answer:

KLM =  55 °
KML =  55 °

Step-by-step explanation:

$$\begin{gathered} MKL=70\text{ ° } \\ MKL+KLM+KML=180\mathrm{°} \\ \delta =90\mathrm{°}-KLM \\ KMX=90-MKL=90-70=20\text{ ° } \\ 2\delta =90\mathrm{°}-KMX \\ \delta =(90-KMX)\mathrm{/}2=(90-20)\mathrm{/}2=35\text{ ° } \\ KLM=90-\delta =90-35=55\text{°} \end{gathered}$$

$KML=180-MKL-KLM=180-70-55=55\text{°}$

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