Obtuse angle

Line OH is the height of the triangle DOM, and line MN is the bisector of angle DMO. the Obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)

Correct answer:

∠ DMO =  60 °

Step-by-step explanation:

$$\begin{gathered} \angle MOH=180°-\alpha -4\alpha =180°-5\alpha \\ 90°+(\alpha +\alpha )+(180°-5\alpha )=180° \\ 90°=3\alpha \\ \alpha =30° \\ \angle DMO=2\alpha =2\cdot 30°=60^{\circ } \end{gathered}$$

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