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:

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

$KML=\angle KML=180-\angle MKL-\angle KLM=180-70-55=55^{\circ }$

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